Question

Fifth Fourth National Bank has a savings program which will guarantee you $14,000 in 10 years if you deposit $105 per month. What APR is the bank offering you on this savings plan? Multiple Choice

2.39%

1.93%

2.32%

2.32%

2.09%

Answer 1

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

Where, P = Annuity = 105, n = Number of Periods = 10*12 = 120, FV = 14000

Therefore,

14000 = 105*[{(1+i)^120}-1]/i

133.33 = [{(1+i)^120}-1]/i

Trying all the options,

2.39:

i = 0.0239/12 = 0.00199

Therefore, [{(1+0.00199)^120}-1]/0.00199 = 135.388

2.32:

i = 0.0232/12 = 0.001933

Therefore, [{(1+0.001933)^120}-1]/0.001933 = 134.9158

2.09:

i = 0.0209/12 = 0.00174

Therefore, [{(1+0.00174)^120}-1]/0.00174 = 133.318

Therefore, i = 2.09%