First Simple Bank pays 6 percent simple interest on its investment accounts. First Complex Bank pays interest on its accounts compounded annually.

Question

Required:
What rate should the bank set if it wants to match First Simple Bank over an investment horizon of 10 years?

Answer 1

Assume an investment of $1.00

First Simple Bank:
amount after 6 years = 1 + PRT
= 1 + 1(.06)(10)
= 1.60

Complex Bank:
1(1+i)^10 = 1.6
take 10th root of both sides

( (1+i)^10)((1/10) = 1.6^(1/10)
1+i = 1.048122..
i = .048122..
or
appr 4.81%