Question

Assume that you contribute $260 per month to a retirement plan for 20 years. Then you are able to increase the contribution to $460 per month for the next 30 years. Given a 6.0 percent interest rate, what is the value of your retirement plan after the 50 years? (Do not round intermediate calculations and round your final answer to 2 decimal places.)

Answer 1

Let’s divide the annuity stream in to two annuities, first one with $ 260 monthly deposits for 50 years and second one with $ 200 monthly deposits for 30 years. We have to compute FV of both annuities and add the results to get the desired retirement fund value.

Formula for future value of annuity is:

FV = P x [(1+r) ⁿ – 1/r]

P = Periodic deposit

r = Rate per period = 6 % i.e. 0.06/12 = 0.005 p.m.

n = Numbers of periods

FV of $ 260 cash flow stream = $ 260 x [(1+0.005) ^50x12 – 1/0.005]

                                                     = $ 260 x [(1.005) ⁶⁰⁰ – 1/0.005]

                                                    = $ 260 x [(19.9359554235189 – 1)/0.005]

                                                    = $ 260 x (18.9359554235189/0.005)

                                                    = $ 260 x 3,787.191084703780

                                                    = $ 984,669.682022982

FV of $ 200 cash flow stream = $ 200 x [(1+0.005) ^30x12 – 1/0.005]

                                                     = $ 200 x [(1.005) ³⁶⁰ – 1/0.005]

                                                    = $ 260 x [(6.02257521226289 – 1)/0.005]

                                                    = $ 260 x (5.02257521226289/0.005)

                                                    = $ 260 x 1,004.51504245258

                                                    = $ 200,903.008490515

Total future value of two cash flow stream = $ 984,669.682022982 + $ 200,903.008490515

                                                                            = $ 1,185,572.690513497 or 1,185,572.69

Value of retirement plan after 50 years is 1,185,572.69