Question

You graduate from College at 21. For your retirement, you decide to invest into a Fidelity mutual fund that gives you a 7.5% APR compounding monthly. After some years of work, you will retire and move the investment into another Vanguard money market account which gives you a 3% APR compounding monthly. During the years of working, you invest $350 every month. You plan to spend $4,500 every month until you pass away. You estimate that you will pass away at 85 years old. When can you retire?

Answer 1

To estimate the age of retirement, the future value of the savings at retirement has to equal to present value of the total monthly spending over retirement, at that age. This can be solved using Solver as follows:

Graduation age (g)	21
Retirement age ('R)	59.7
Number of years of working	38.7	Number of years of retirement (85-R)	25.3
PMT	350	PMT	4500
N	465	N	303
APR	7.50%	APR	3%
rate	0.625%	rate	0.250%
FV	9,56,200.38	PV	9,56,200.38
FV - PV	(0.00)

Formulas:

One can retire approximately at the age of 59.7 years. (Note: There is no exact answer to this question.)