(5 points) Suppose you invest a $12,000 lump sum amount for 25 years at a nominal interest rate of 8%, compounded semi-annually

Finance Aug 05, 2020

(5 points) Suppose you invest a $12,000 lump sum amount for 25 years at a nominal interest rate of 8%, compounded semi-annually. (a) Use the interest rate per compounding period to calculate the future worth of this investment at EOY 25. (b) Use the effective interest rate to calculate the future worth of this investment at EOY 25. Show all work.

Expert Solution

PV = 12,000

Interest rate = 8% per year compounded semi-annually

a) Interest rate per compounding period = 8%/2 = 4% semi-annual rate

n = 25 * 2 = 50 semi-annual periods

FV = PV * (1 + r)^n

FV = 12,000 * (1 + 0.04)^50

FV = $85,280.2001553397

b) Effective annual interest rate, r = (1 + 0.08/2)^2 - 1

r = 0.0816

FV = PV * (1 + r)^n

n = 25

FV = 12,000 * (1 + 0.0816)^25

FV = $85,280.2001553397

Note that they both result in the same answer

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