A note pays five percent annual simple interest. What value does the rate take when it is entered into the simple interest formula?

Five, the percentage figure as stated, with the resulting interest read as a percentage of principal.

Zero point zero five, the percentage converted to its decimal equivalent.

Zero point five, the percentage shifted one place so that the answer emerges in dollars.

Zero point zero zero five, the percentage divided by one thousand to match the formula's scale.

A lender quotes simple interest at one percent per month on a loan with an eighteen-month term. What value must T take in the simple interest formula?

Eighteen, because the time must be stated in the same unit as the rate.

One point five, since T in the simple interest formula is always a number of years.

Twelve, the months in a year, the eighteen-month term entering through the rate instead.

Zero point one eight, the term divided by one hundred to match the decimal rate.

Fifty thousand dollars is lent at eight percent annual simple interest for a term of nine months. How much simple interest does the loan produce over that term?

Thirty-six thousand dollars, the nine months entering the formula as nine whole periods at the annual rate of eight percent.

Three thousand dollars, the nine months entering the formula as zero point seven five of a year.

Four thousand dollars, the full annual interest, since an annual rate is earned in full whenever it is quoted.

Five thousand three hundred and thirty-three dollars, the term entered as twelve divided by nine rather than nine divided by twelve.

A borrower repays the principal together with all accrued simple interest in a single payment at the end of the term. Which expression gives that single total amount?

The rate multiplied by the time and then raised to the power of the principal invested.

The principal compounded at the rate for every period in the term, each period's interest joining the base.

The principal added to the rate, then multiplied by the time and by one hundred.

An investor deposits ten thousand dollars in a savings certificate paying five percent annual simple interest for three years. How much interest does the certificate earn in its third year?

Five hundred and fifty-one dollars, more than the first year because the earlier interest is itself earning.

Five hundred and twenty-five dollars, the rate applied to the ten thousand five hundred standing at the start of the year.

One thousand five hundred dollars, the whole term's interest falling due in the final year.

Five hundred dollars, the same amount it earned in its first year.

A Treasury bill is bought for ninety-eight thousand dollars and matures at a face value of one hundred thousand dollars ninety-one days later. On the money market Actual/360 basis, what annualised simple interest rate has the buyer earned on the amount actually invested?

About eight point zero eight percent, the two thousand dollar gain measured against the ninety-eight thousand paid.

About seven point nine one percent, the gain measured against the one hundred thousand dollar face value.

About eight point one six percent, the ninety-one day return multiplied by four quarters of a year.

About two point zero four percent, the gain measured against the price paid but never annualised.

Interest on short-term money market instruments is computed on a simple interest basis rather than a compound basis. What accounts for that convention?

These instruments are quoted at a discount to face value, and a discount price cannot be compounded arithmetically.

Compounding within so short a term changes the amount immaterially, and linear accrual is simpler and more transparent.

Compound interest would produce the smaller amount over so short a term, so the simple basis protects the lender.

Compounding is barred on any instrument whose interest is paid in one payment at maturity rather than periodically.

The same ninety-day period is measured first under the Actual/360 day count convention and then under Actual/365. What fraction of a year does each convention assign to it?

Twenty-five percent under both, each convention counting the ninety actual calendar days in the period.

Twenty-four point six six percent under Actual/360 and twenty-five percent under Actual/365.

Twenty-five percent under Actual/360 and twenty-four point six six percent under Actual/365.

Twenty-four point six six percent under both, the ninety days being divided by a calendar year in each case.

An investor who has held a fixed-rate corporate bond for ten years compares the coupon payment now arriving with the first coupon received after buying it. Why is the payment arriving now identical in amount to that first one?

The issuer pays a level amount of early interest and later principal, so the instalments are equal by design.

Each coupon is compound interest on a base that resets to face value at every payment date, cancelling the growth.

The coupon is recalculated at each date against the market price, which has returned to face value over ten years.

Each coupon is simple interest on an unchanged face value, so no earlier coupon ever enters the base.

A credit card discloses an annual percentage rate of eighteen percent and adds any unpaid interest to the balance each month. Over a year in which the cardholder pays nothing at all, what annual cost does the balance actually bear?

About nineteen and a half percent, because the interest added each month itself bears interest for the rest of the year.

Exactly eighteen percent, because the disclosed annual percentage rate is the only figure the issuer is contractually permitted to charge.

About sixteen and a half percent, because the interest added late in the year has little time left in which to accrue further.

About thirty-six percent, because interest is charged on the original balance and then again on the whole of the year's accumulated interest.

The SEC obtains an order disgorging a defendant's gains and also seeks prejudgment interest running over several years. How is that interest computed in most SEC enforcement cases?

As compound interest on the disgorgement principal, each period's interest joining the base for the periods that follow.

As simple interest on the disgorgement principal, so interest already accrued never joins the base.

As simple interest on the defendant's total trading profits, including gains the order does not require to be disgorged.

As compound interest for the years before the complaint and simple interest for the years after it was filed.

Prejudgment interest on an SEC disgorgement amount is computed at the Internal Revenue Service underpayment rate. Over what period does that interest run?

From the filing of the Commission's complaint through the date of the court order.

From the date of the violation through the date the defendant pays the amount in full.

From the filing of the Commission's complaint through the date the defendant pays in full.

A supply contract says nothing about interest on late payments, and the buyer pays ninety days after the due date. How does interest on the overdue amount accrue?

At no rate at all, because a contract fixing no rate for late payment creates no entitlement to interest.

At a rate the Uniform Commercial Code fixes nationally, computed as simple interest on the overdue amount.

At the rate applicable state law specifies, compounded monthly until the overdue amount is paid in full.

At the rate applicable state law specifies, computed as simple interest on the overdue amount.

A borrower takes a four-year loan carrying simple interest, and the lender computes I as P times R times T. What does I measure?

The interest owed for one year of the term, to be multiplied by four for the whole loan.

The total the borrower repays at maturity, the principal and all of its interest together.

The total interest owed over the whole four-year term, the product of the three variables.

The average interest owed per year, the four years' interest divided by the length of the term.

A lender wants to earn one thousand dollars of simple interest on eight thousand dollars lent at five percent a year. For how long must the money be lent?

Two and a half years, the interest divided by the product of the principal and the annual rate.

About two point four years, each year's interest joining the principal before the following year's interest is computed.

Eight years, the principal divided by the interest the lender wants the loan to earn over its term.

Zero point four years, the principal multiplied by the annual rate and then divided by the interest the lender wants.

A borrower takes a twenty-four thousand dollar loan at six percent annual simple interest for four years and pays no interest at all until maturity. By the start of the fourth year, four thousand three hundred and twenty dollars of interest has built up unpaid. On what amount is the fourth year's interest computed?

Twenty-eight thousand three hundred and twenty dollars, the principal together with all of the interest left unpaid so far.

Twenty-four thousand dollars, the original principal, however much interest has built up unpaid.

Twenty-five thousand four hundred and forty dollars, the principal together with the unpaid interest of the most recent year.

About twenty-eight thousand five hundred and eighty-four dollars, the principal grown at six percent compounded over the three years elapsed.

A lender quotes simple interest of two percent per quarter on a forty thousand dollar loan with a twenty-one-month term. How much interest does the loan produce over the term?

One thousand four hundred dollars, the twenty-one months entering the formula as one and three quarter years.

Sixteen thousand eight hundred dollars, the twenty-one months entering the formula as twenty-one periods.

Five thousand six hundred dollars, the twenty-one months entering the formula as seven quarters.

Three thousand two hundred dollars, the quarterly rate applied across the four quarters of a single year.

A borrower takes thirty thousand dollars for six months at seven percent annual simple interest, repaying principal and interest together in one payment at the end. How much is that payment?

Thirty-two thousand one hundred dollars, a full year's interest being due because the rate is quoted annually.

About thirty-one thousand and sixty-five dollars, the half-year's interest compounded monthly over the six months.

Forty-two thousand six hundred dollars, the six months entering the formula as six whole periods at the annual rate.

Thirty-one thousand and fifty dollars, half a year's interest added to the thirty thousand borrowed.

A commercial paper note with a face value of five hundred thousand dollars runs sixty days at an annual simple interest rate of six percent. On the money market Actual/360 basis, how much interest does the note pay for its term?

Five thousand dollars, the sixty days entering the formula as sixty over three hundred and sixty.

Ten thousand dollars, the sixty days entering the formula as sixty over the one hundred and eighty days of a half-year.

Thirty thousand dollars, a full year's interest because the note's rate is quoted as an annual rate.

Seven thousand five hundred dollars, the sixty days rounded up to the ninety-day quarter on which money market rates are quoted.

A money market instrument's yield is quoted at four point five percent on the Actual/360 day count basis. An analyst restates it as a bond equivalent yield to compare it with instruments quoted on a three hundred and sixty-five day year. What figure results?

About four point four four percent, the quote cut by a factor of three hundred and sixty over three hundred and sixty-five.

About four point five six percent, the quote raised by a factor of three hundred and sixty-five over three hundred and sixty.

Four point five percent unchanged, both bases counting the same actual calendar days in the period.

About four point five nine percent, the quote compounded monthly over the twelve months of a year.

A fixed-rate bond pays its coupon twice a year. How is the amount of each of those payments determined?

Half of the annual coupon rate multiplied by the price the holder paid for the bond.

Half of the bond's yield to maturity multiplied by the bond's face value.

Half of the annual coupon rate multiplied by the bond's face value.

The half-yearly rate that compounds to the annual coupon rate, multiplied by face value.

An investor buys a fixed-rate corporate bond at a price giving a stated yield to maturity, holds it to maturity and reinvests every coupon. Soon after purchase, market rates rise and stay higher for the rest of the bond's life. How does the investor's realised total return compare with the yield promised at purchase?

It equals the promised yield, because the coupons are fixed by contract whatever market rates do afterwards.

It is lower, because the rise in rates pushes the bond's price below what the investor paid for it.

It is higher, because the coupon payments are reset upward in step with the rise in market rates.

It is higher, because the coupons are reinvested at rates above the yield the calculation assumed for them.

A loan of fifteen thousand dollars at a fixed annual simple interest rate produces three thousand six hundred dollars of interest over four years. With the same principal and rate, how much interest does an eight-year term produce?

Seven thousand two hundred dollars, twice the four-year figure, since each year adds the same amount.

About eight thousand nine hundred and eight dollars, each year's interest joining the balance on which the next is charged.

About six thousand four hundred dollars, the later years earning less as the rate is spread over a longer term.

Fourteen thousand four hundred dollars, four times the four-year figure because the term and each year's interest both double.

Fourteen thousand dollars is invested at five percent a year for three years. Simple interest yields two thousand one hundred dollars, and annual compounding yields two thousand two hundred and six dollars and seventy-five cents. What does the difference of one hundred and six dollars and seventy-five cents consist of?

A higher effective annual rate earned on the original fourteen thousand dollars throughout the three years.

Interest earned in the second and third years on interest accrued in the years before them.

Interest earned on the original principal in the third year, the year in which compounding first takes effect.

Interest on the fourteen thousand dollars for the days of each year that the simple calculation leaves out.

Four amounts appear in a client's annual review. Which one is calculated as simple interest rather than compound interest?

The ten-year growth of a stock holding whose dividends have been reinvested throughout.

The rise over several years of a fund whose capital appreciation builds on a growing base.

The interest a bankers acceptance the client holds pays over its term.

A card balance to which a year's unpaid interest has been added month by month.

A credit card charges a periodic rate each month. How is the annual percentage rate it discloses derived from that monthly rate?

The monthly rate compounded over twelve months, allowing for interest added to the balance.

The rate the card charged in its most recent month, carried forward without annualising it.

The monthly rate averaged over the past twelve statements, whatever rate applied in each.

The monthly rate multiplied by twelve, with no allowance for interest added to the balance.

Two savings accounts both quote a nominal annual rate of four point eight percent; one adds interest to the balance daily and the other once a year. How do the annual percentage yields disclosed for the two accounts compare?

The daily account's yield is higher, since the yield reflects how many times a year interest is added to the balance.

Both yields are four point eight percent, since a yield restates the nominal rate that the two accounts share.

The annual account's yield is higher, since its single credit applies the full rate to a whole year's balance at once.

Both yields are equal and above four point eight percent, since each account adds interest at least once a year.

A payment of thirteen thousand four hundred and eighty-three dollars and twenty cents is due two years from now. Discounted at six percent a year compounded annually, what is its present value?

About twelve thousand and thirty-nine dollars, the payment divided by one plus six percent multiplied by two.

Twelve thousand dollars, the payment divided by one point zero six raised to the second power.

About eleven thousand eight hundred and sixty-five dollars, the payment reduced by six percent of itself for each of the two years.

Twelve thousand seven hundred and twenty dollars, the payment divided by one point zero six for a single year.

Two analysts each want a quick future-value estimate: one for a deposit held sixty days, the other for a sum left invested for twenty-five years. For which estimate is the simple interest future value formula appropriate?

The twenty-five-year sum, where the long horizon averages out the effect of compounding across the many years.

Both estimates, since simple and compound future values agree with each other whenever the rate stays fixed.

The sixty-day deposit, where ignoring compounding within so short a period leaves an immaterial error.

Neither estimate, since a future value must always be calculated on a compound basis however short the period.

Simple Interest — The I Equals PRT Formula Explained

Simple Interest

Simple interest is the method of calculating the cost of borrowing or the return on lending by applying a fixed interest rate exclusively to the original principal amount for each period of the loan or investment, never incorporating previously accrued interest into the base on which future interest is calculated. It is the most fundamental and mathematically straightforward form of interest calculation in finance — the interest earned or owed in any given period is identical to every other period of the same duration, because the base upon which the calculation is applied never changes.

Simple interest forms the conceptual foundation upon which understanding of compound interest, the time value of money, and all more complex interest and present value calculations is built — and it governs the actual interest mechanics of several directly important financial instruments including coupon-paying bonds, commercial paper, bankers acceptances, and the money market conventions for calculating interest on short-term instruments. It is tested on the SIE and Series 7 examinations in the context of basic interest calculations, the time value of money framework, and the distinction from compound interest.

The Formula — I Equals PRT

The simple interest formula has three variables — principal, rate, and time — whose product produces the total interest amount.

Simple interest equals principal multiplied by rate multiplied by time.

I equals P multiplied by R multiplied by T.

Principal — P — is the original amount of money lent, borrowed, or invested. It is the base amount on which interest is calculated for every period of the arrangement and remains constant throughout the life of the simple interest calculation. Under compound interest, the principal grows each period as accrued interest is added to it — under simple interest, the principal never changes.

Rate — R — is the interest rate expressed as a decimal or percentage per unit of time, almost always expressed as an annual rate. A five percent annual rate is expressed as zero point zero five in the formula. It is critical that the rate and the time period be expressed in the same time unit — if the rate is annual, the time must be expressed in years or fractions of years. If the rate is monthly, the time must be expressed in months.

Time — T — is the number of periods for which the interest calculation applies, expressed in the same unit as the rate. One year at an annual rate produces T equals one. Six months at an annual rate produces T equals zero point five or six-twelfths. Ninety days at an annual rate using the money market Actual/360 day count convention produces T equals ninety divided by three hundred and sixty.

The total amount owed or received at the end of the period — principal plus interest — equals the principal plus the simple interest, or equivalently the principal multiplied by the quantity one plus the rate multiplied by time.

Total amount equals principal multiplied by one plus rate multiplied by time.

Total amount equals P multiplied by the quantity one plus R times T.

Worked Examples — From Simple to Applied

Three worked examples illustrate the formula across progressively more applied contexts.

Example one — the basic calculation. An investor deposits ten thousand dollars in a savings certificate at a five percent annual simple interest rate for three years. Simple interest equals ten thousand multiplied by zero point zero five multiplied by three — equalling one thousand five hundred dollars. Total value at maturity equals ten thousand plus one thousand five hundred — equalling eleven thousand five hundred dollars. The investor earns five hundred dollars of interest in each of the three years — interest in year one, year two, and year three is identical because the calculation never incorporates prior interest into the base.

Example two — the fractional year calculation. A commercial paper note with a face value of one million dollars is issued at a discount rate equivalent to an annual simple interest rate of four and a half percent with a term of ninety days. Using the money market Actual/360 day count convention, T equals ninety divided by three hundred and sixty, equalling zero point two five. Simple interest equals one million multiplied by zero point zero four five multiplied by zero point two five — equalling eleven thousand two hundred and fifty dollars. The note pays eleven thousand two hundred and fifty dollars of interest for its ninety-day term.

Example three — solving for the rate. A three-month Treasury bill is purchased for ninety-eight thousand dollars and matures at face value of one hundred thousand dollars in ninety-one days.

The interest earned is two thousand dollars. Using the Actual/360 convention, the simple interest rate equals interest divided by principal divided by time — two thousand divided by ninety-eight thousand divided by ninety-one divided by three hundred and sixty — equalling approximately eight point zero eight percent annualised. This calculation demonstrates how the simple interest formula is inverted to solve for the unknown rate — the technique used to compute the bond equivalent yield on Treasury bills.

Simple Interest and the Money Market Day Count Conventions

The money market — the market for short-term debt instruments with original maturities of one year or less — calculates interest using simple interest rather than compound interest, because the short-term nature of the instruments makes compounding within the term immaterial and because market convention favours the transparency and calculational simplicity of linear interest accrual.

United States dollar money market instruments — Treasury bills, commercial paper, bankers acceptances, federal funds, and repurchase agreements — use the Actual/360 day count convention. Under this convention, the number of calendar days in the actual period is counted precisely, and that actual count is divided by a 360-day year rather than the actual 365 or 366-day calendar year. The Actual/360 convention treats a given period as a larger fraction of the year than an Actual/365 calculation does — a ninety-day period represents ninety divided by three hundred and sixty, equalling twenty-five percent of the year under Actual/360, compared to only ninety divided by three hundred and sixty-five, equalling twenty-four point six six percent under Actual/365. Because the same dollar interest is spread across a larger fraction of a year, a rate quoted on an Actual/360 basis is lower than the equivalent rate quoted on an Actual/365 basis — which is why a money market yield quoted on Actual/360 is multiplied by three hundred and sixty-five divided by three hundred and sixty to arrive at its bond equivalent yield. This difference is small but meaningful for precise comparison of returns across instruments using different day count conventions.

United States Treasury notes and bonds — longer-term instruments — use the Actual/Actual day count convention for interest accrual calculations, counting the exact number of calendar days and dividing by the exact number of days in the coupon period. Corporate bonds in the United States traditionally use the Thirty/Three Sixty day count convention — also called the Thirty over Three Sixty convention — which assumes every month has exactly thirty days and every year has exactly three hundred and sixty days, producing predictable and uniform coupon payment amounts.

Understanding day count conventions is important for Series 7 examination candidates because the accrued interest calculation on bonds — the interest that has accrued since the last coupon payment and that must be paid by the buyer to the seller in a secondary market bond transaction — depends directly on which day count convention the bond uses.

Simple Interest and Coupon-Paying Bonds — The Direct Application

The most practically important application of simple interest in the securities markets is the coupon payment structure of fixed income securities. Every coupon payment on a bond is a simple interest calculation — the coupon rate multiplied by the face value of the bond equals the annual interest payment, and each semiannual payment equals half of the annual coupon amount regardless of how long the investor has held the bond.

A ten thousand dollar face value corporate bond with a six percent annual coupon rate pays three hundred dollars every six months — six percent of ten thousand is six hundred dollars per year, divided by two for the semiannual payment frequency, equalling three hundred dollars per payment. This three hundred dollar payment is identical at every coupon date throughout the bond's life — it does not increase as each coupon payment is received, because coupons are simple interest payments calculated on the unchanged face value rather than compound interest that accumulates on a growing base.

This simple interest structure of coupon payments is what gives rise to reinvestment risk — the risk discussed in the Reinvestment Risk entry of this dictionary — because the yield to maturity calculation assumes that each coupon received can be reinvested at the same yield to maturity rate. If actual reinvestment rates differ from the yield to maturity, the investor's realised total return differs from the promised yield, and that difference is entirely attributable to the compounding assumption embedded in the yield calculation rather than to the simple interest coupon payments themselves.

Simple Interest Versus Compound Interest — The Critical Distinction

The distinction between simple interest and compound interest is among the most foundational and most tested concepts in the SIE and Series 7 examination framework — understanding precisely how the two differ and in which circumstances each applies is essential for both examination success and practical financial analysis.

Simple interest calculates interest exclusively on the original principal for every period — the interest earned in period two is identical to the interest earned in period one because neither period's interest is incorporated into the base for subsequent calculations. The total interest over any number of periods is a linear function of time — doubling the time period exactly doubles the total interest. This linear relationship is the defining mathematical characteristic of simple interest.

Compound interest calculates interest on the principal plus all previously accrued interest — each period's interest becomes part of the base for the following period's calculation, creating an exponentially growing interest amount. The total interest over a given period under compounding is always greater than under simple interest for the same principal, rate, and time, because compound interest includes interest on interest. The longer the time period and the higher the compounding frequency, the greater the difference between compound and simple interest for the same nominal rate.

A comparison using a ten thousand dollar principal at six percent annual interest makes the distinction precise. Under simple interest over five years, total interest equals ten thousand multiplied by zero point zero six multiplied by five — equalling three thousand dollars. Under annual compounding over five years, total interest equals ten thousand multiplied by the quantity one plus zero point zero six raised to the fifth power, minus ten thousand — equalling ten thousand multiplied by one point three three eight two three, minus ten thousand — equalling three thousand three hundred and eighty-two dollars and twenty-six cents. The compound interest produces three hundred and eighty-two dollars and twenty-six cents more over five years — the dollar amount of interest earned on previously accrued interest.

The practical significance of this distinction for securities professionals is that almost all investment returns over periods longer than one year compound — dividends reinvested, coupon payments reinvested, and capital appreciation that compounds on a growing base all follow compound rather than simple interest mechanics — while the quoted yields on money market instruments and the stated coupon rates on bonds follow simple interest conventions for their periodic payment calculations.

The Annual Percentage Rate Versus the Annual Percentage Yield

The distinction between the annual percentage rate and the annual percentage yield — sometimes called the effective annual rate — directly reflects the distinction between simple and compound interest and is tested in the context of consumer financial disclosures.

The annual percentage rate — APR — is the simple interest expression of the cost of credit, calculated as the periodic rate multiplied by the number of periods in a year without compounding. A credit card that charges one and a half percent monthly has an APR of eighteen percent — one and a half percent multiplied by twelve. This APR represents the simple interest annualised rate without accounting for the compounding that occurs when unpaid interest is added to the balance each month.

The annual percentage yield — APY — or effective annual rate — is the compound interest expression that accounts for the frequency of compounding — how many times per year interest is added to the principal and begins earning interest on itself. The APY for the same one and a half percent monthly rate equals the quantity one plus zero point zero one five raised to the twelfth power, minus one — equalling approximately nineteen point five six percent — materially higher than the eighteen percent APR because the APY captures the effect of monthly compounding on the annualised cost.

The Truth in Lending Act — Regulation Z at 12 CFR Part 1026 — requires creditors to disclose the APR in consumer credit transactions, allowing borrowers to compare the cost of credit across different lenders and product types on a standardised basis. The APY is required to be disclosed for deposit accounts under the Truth in Savings Act — Regulation DD — allowing depositors to compare the return on savings products that compound at different frequencies.

Simple Interest in Regulatory and Legal Contexts

Simple interest appears in regulatory and legal contexts beyond its role in investment calculations — particularly in the context of disgorgement and prejudgment interest in SEC enforcement proceedings and in the calculation of interest on defaulted obligations.

When the SEC brings an enforcement action and obtains disgorgement of a defendant's ill-gotten gains, it typically also seeks prejudgment interest on the disgorged amount — calculated from the date of the violation through the date of the court order at the Internal Revenue Service underpayment rate under IRC Section 6621. This prejudgment interest is calculated as simple interest rather than compound interest in most SEC enforcement cases — applied to the principal disgorgement amount at the applicable quarterly IRS rate for each quarter from the violation date through judgment.

In contract law, the default rate of interest on overdue obligations — when no specific rate has been agreed in the contract — is governed by applicable state law, which typically specifies a simple interest rate. The Uniform Commercial Code's provisions on interest on defaulted payment obligations generally adopt simple interest as the default calculation method in the absence of contractual specification.

The Time Value of Money — Where Simple Interest Sits in the Broader Framework

Simple interest is the foundational concept from which the time value of money framework — the core analytical infrastructure of finance — is built, but the full time value framework almost always uses compound interest rather than simple interest for multi-period calculations because compound interest more accurately reflects the economic reality of money's ability to earn returns on returns.

The present value and future value relationships for single cash flows — discussed in the Present Value and Future Value entries of this dictionary — use compound interest. The present value of a future amount equals the future amount divided by the quantity one plus the discount rate raised to the power of the number of periods. The future value of a present amount equals the present amount multiplied by one plus the interest rate raised to the number of periods. Both formulas reflect compounding — the exponential relationship between present and future value that makes compound interest the appropriate tool for multi-period financial analysis.

Simple interest future value — where the future amount equals the principal multiplied by one plus rate multiplied by time — is a linear rather than exponential function and is appropriate only for single-period or very short-term calculations where the approximation error from ignoring compounding within the period is immaterial. The money market conventions discussed above — Actual/360 for Treasury bills and commercial paper — use simple interest precisely because the short maturities of money market instruments make compounding within the term economically immaterial.

Examination Relevance and Key Takeaways

Simple interest is tested on the SIE and Series 7 examinations in the context of the interest calculation framework, the time value of money, the distinction from compound interest, and the money market conventions for short-term instruments.

The key points to retain are these.

Simple interest equals principal multiplied by rate multiplied by time — I equals P times R times T. The principal never changes in a simple interest calculation — interest is always computed on the original amount borrowed or invested, not on a growing balance that includes previously accrued interest. Total amount at maturity equals principal plus interest — or equivalently principal multiplied by one plus rate multiplied by time — P multiplied by the quantity one plus R times T.

The rate and time must be expressed in the same time unit — an annual rate requires time expressed in years or fractions of years. Money market instruments in the United States use the Actual/360 day count convention — dividing the actual number of days in the period by three hundred and sixty to express the time fraction. Corporate bonds use the Thirty/Three Sixty day count convention. Treasury notes and bonds use the Actual/Actual convention. Coupon payments on bonds are simple interest calculations — the stated coupon rate multiplied by the face value produces the annual interest regardless of whether the investor reinvests those coupons.

Simple interest produces a linear relationship between time and interest — doubling the time exactly doubles the interest. Compound interest produces an exponential relationship — interest earned on previously accrued interest causes total interest to grow faster than linearly with time. For the same principal, rate, and time period, compound interest always produces more total interest than simple interest — the difference equals the interest earned on prior interest.

The annual percentage rate is the simple interest expression of credit cost — required by the Truth in Lending Act and Regulation Z at 12 CFR Part 1026 for consumer credit disclosures.

The annual percentage yield is the compound interest expression capturing the effect of compounding frequency — required for deposit account disclosures. Prejudgment interest in SEC enforcement proceedings is typically calculated as simple interest at the IRS underpayment rate under IRC Section 6621 applied to the disgorged principal amount from the date of violation through the date of judgment.