Question

If you start making $265 monthly contributions today and continue them for four years, what is their future value if the compounding rate is 9.75 percent APR? What is the present value of this annuity?

Answer 1

APR = 9.75%
Monthly Interest Rate = 9.75%/12
Monthly Interest Rate = 0.8125%

Monthly Contribution = $265
Period = 4 years or 48 months

Future Value = $265*1.008125^48 + $265*1.008125^47 + $265*1.008125^46 + ... + $265*1.008125
Future Value = $265 * 1.008125 * (1.008125^48 - 1) / 0.008125
Future Value = $265 * 58.89375
Future Value = $15,606.84

Present Value = $265 + $265/1.008125 + $265/1.008125^2 + $265/1.008125^3 + ... + $265/1.008125^47
Present Value = $265 * 1.008125 * (1 - (1/1.008125)^48) / 0.008125
Present Value = $265 * 39.93730
Present Value = $10,583.38