Question

Michael invests $100 into a savings account. After 5 years, he closes the account and withdraws his balance of $124. Assuming simple interest, what is the annual interest rate?

Assuming that interest is compounded semiannually, what is the annual interest rate?

Answer 1

Simple Interest = Amount Withdrawn - Principal Amount

= $ 124 - $ 100

= $ 24

Simple Interest = Principal * Rate of Interest * Time

$ 24 = $ 100 * Rate of Interest * 5

Rate of Interest = $ 24 /$ 500

= 4.80%

Hence the correct answer is 4.80%

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Computing the Semi Annual Rate of Interest:

Future Value = Principal * ( 1+ Rate of Interest) ^ Time

$ 124 = $ 100 * ( 1+ Rate of Interest ) ^ 10

$ 124 / $ 100 = ( 1+ Rate of Interest ) ^ 10

( $ 124 / $ 100) ^ ( 1/10) = 1+ Rate of Interest

[ ( $ 124 / $ 100) ^ ( 1/10) - 1 ] =Rate of Interest

Semi Annual Rate of Interest = 2.174417042%

Hence, the Annual Interest Rate = Semi Annual Rate of Interest * 2

= 2.174417042% * 2

= 4.348834084%

Hence the correct answer is 4.35%