Question

Compute the nominal annual rate of interest (compounded monthly) at which $175.00 deposited at the end of each month for eight years will amount to $30 000.00. Calculate to two decimals. Enter as follows: 12.34% = 12.34

Answer 1

FV of Annuity = P*[{(1+i)^n}-1]/i

Where, FV = 30000, P = Annuity = 175, n = Number of Periods = 8*12 = 96

Therefore,

30000 = 175*[{(1+i)^96}-1]/i

[{(1+i)^96}-1]/i = 30000/175 = 171.42857

By Trial & Error,

Taking i = 0.01, [{(1+0.01)^96}-1]/0.01 = 159.92729

Taking i = 0.011, [{(1+0.011)^96}-1]/0.011 = 168.938

Taking i = 0.0113, [{(1+0.0113)^96}-1]/0.0113 = 171.76

Taking i = 0.01127, [{(1+0.01127)^96}-1]/0.01127 = 171.4764

Therefore, i = 0.01127(approx)

Therefore, Monthly Nominal Interest Rate = 0.01127 = 1.127%

Therefore, Annual Nominal Interest Rate = 0.01127*12 = 0.13524 = 13.52% = 13.52