Compound Interest

Question

ind the accumulated value of an investment of $25,000

for 7

years at an interest rate of 7%

if the money is a. compounded​ semiannually;

b.

compounded​ quarterly;

c.

compounded monthly

d. compounded continuously. Round answers to the nearest cent.

Answer 1

A = P(1+r/a^')^t', where A=final amount, P=original principal, r=interest rate (proportion), a = adjustment factor, and t^'=time in appropriate units

P=$25,000, r=7% = 0.07 and t=7 years.

a. Semiannually mans every 1/2 year so a = 2 and t^' = 7*2 = 14.

A = 25,000(1+0.07/2)¹⁴ = $40,467.36.

b. Quarterly means every 3 months, so a=4 and t^' = 7*4 = 28

A = 25,000(1+0.07/4)²⁸ = $40,635.32

c. Monthly means a=12 and t^' = 7*12 = 84

A = 25,000(1+0.07/12)⁸⁴ = $40,749.85

d. Continuous compounding uses a different formula,

A = Pe^rt = 25,000e^0.07*7 = 25,000e^0.49 = $40,807.91