Question

Vanscoy Bank pays 7.6% simple interest on its investment accounts. If Vade Bank pays interest on its accounts compounded annually, what rate should the bank set if it wants to match Vanscoy Bank over an investment horizon of ten years?

Answer 1

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Answer:

Total Interest on $100 paid by First simple bank for 10 years = $100 * 7.6% * 10 years = $76

Future value of investment after 10 years = $100 + $76 = $176

Future value required by First Complex bank after 10 years = $176

Let the rate of interest by first complex bank be r

Future value = Investment * ( 1 +r)ⁿ

$176 = $100 * (1+r)¹⁰

(1+r)¹⁰ = $176/$100 = 1.76

1+r = 1.76^1/10

r = 1.05816 - 1 = 0.05816 = 5.816%