Single Payment Compound Interest Formulas (other periods) (2024)

Interest and Equivalence

Single payment compound interest formulas (other periods)

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If the interest period andcompounding period are not stated, then the interest rate is understood to beannual with annual compounding. Examples:

"12% interest"means that the interest rate is 12% per year, compounded annually.

"12% interest compoundedmonthly" means that the interest rate is 12% per year (not 12% per month),compounded monthly. Thus, the interest rate is 1% (12% / 12) per month.

"1% interest per monthcompounded monthly" is unambiguous.

When the compounding periodis not annual, problems must be solved in terms of the compounding period, notyears.

Example: If $100 is investedat 6% interest, compounded monthly, then the future value of this investmentafter 4 years is:

F = P (1 + i) ⁿ =$100 (1 + 0.005) ⁴⁸

= $100 (1.005) ⁴⁸= $100 (1.2705) = $127.05

Note that the interest rateused above is (6% / 12) = 0.5% per month = 0.005 per month, and that the numberof periods used is 48 (months), not 4 (years).

Interest and Equivalence

Single payment compound interest formulas (other periods)

Question 1

Question 2

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Question 1.

Use interest tables. Supposethat $1,000 is invested for 4 years at an interest rate of 12%, compoundedquarterly. How much will be in the account at the end of 4 years?

Choose an answer by clicking on one of the letters below, or click on"Review topic" if needed.

A F = $1,000 (F/P,12%,4) = $1,000 (1.574) = $1,574

B F = $1,000 (F/P,12%,16) = $1,000 (6.130) = $6,130

C F = $1,000 (F/P,3%,4) = $1,000 (1.126) = $1,126

D F = $1,000 (F/P,3%,16) = $1,000 (1.605) = $1,605

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Question 2.

Use interest tables. How muchmust be invested now at 6% interest, compounded monthly, to accumulate $1,000at the end of five years?

Choose an answer by clicking on one of the letters below, or click on"Review topic" if needed.

A P = $1,000 (P/F,6%,60) = $1,000 (0.0303) = $30.30

B P = $1,000 (P/F,0.5%,60) = $1,000 (0.7414) = $741.37

C P = $1,000 (P/F,0.5%,5) = $1,000 (0.9754) = $975.40

D P = $1,000 (P/F,6%,5) = $1,000 (0.7473) = $747.30

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