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.

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 5 years at an interest rate of 5% if the money is a. compounded​ semiannually; b. compounded​ quarterly; c. compounded​ monthly; d. compounded continuously.

Answer 1

You would be solving for "A" in each equation. P = 15000, t = 5, r = 0.05

For a, b, and c, use the first equation A = P(1 + r/n)^nt

In the case of "compounded​ semiannually" n = 2 meaning the equation is:

A = 15000(1 + 0.05/2)⁽²⁾⁽⁵⁾

A = 15000(1 + 0.025)¹⁰

A = 15000(1.025¹⁰)

A = $19,201.27

Compounded quarterly means n = 4

Compounded monthly means n = 12

Compounded continuously means use the 2nd equation:

A = Pe^rt

A = 15000e^(0.05)(5)

A = 15000e^0.25

A = 15000(1.284025)

A = $19,260.38