Question

Use the compound interest formulas A=P(1+r/n)^nt and A=Pe^rt to solve the problem given. Round answers to the nearest cent.

Find the accumulated value of an investment of $15,000 for 6 years at an interest rate of 4% if the money is a. compounded
semiannually; b. compounded quarterly: c. compounded monthly d. compounded continuously.

Answer 1

a) $19,023.63

b) $19,046.02

c) $19,061.13

d) $19,068.74

Explanation:

P = 15000

t = 6

r = 0.04

a) Compounded semiannually means 2 times per year, so n = 2.

A = 15000 (1 + 0.04/2)^(2×6)

A = 19023.63

b) Compounded quarterly means 4 times per year, so n = 4.

A = 15000 (1 + 0.04/4)^(4×6)

A = 19046.02

c) Compounded monthly means 12 times per year, so n = 12.

A = 15000 (1 + 0.04/12)^(12×6)

A = 19061.13

d) Compounded continuously means we use the continuous equation:

A = 15000 e^(0.04×6)

A = 19068.74