What is the initial amount of money needed to end up with $12125 in five years if it is invested at 18% annually but compounded monthly? What is the effective annual interest rate?

What is the initial amount of money needed to end up with $12125 in five years if it is invested at 18% annually but compounded monthly? What is the effective annual interest rate?
Answer:

18% annual interest rate (R) = (18/12) = 1.5% monthly interest rate

Number of months (N) = 5 x 12 = 60

If initial amount be P, then

P x (1 + R)N = Future amount

P x (1.015)60 = $12,125

P x 2.4432 = $12,125

P = $4,963

Effective interest rate (EAR) = [1 + (Annual rate / M)]M – 1

Where

M: Number of compounding periods per year = 12

EAR = [1 + (0.18 / 12)]12 – 1 = (1.015)12 – 1 = 1.1956 – 1 = 0.1956

EAR = 19.56%

Asked on February 15, 2018 in economics.
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