Question

You want to come up with a plan to save for retirement. You will contribute to your retirement account monthly for 40 years. One month after your last contribution you will begin monthly withdrawals of $7,500 from that retirement account. You earn 6.6% APR while you’re contributing to your retirement savings and 3.6% APR while you are withdrawing. You want to have enough money to finance 35 years in retirement. (Assume compounding frequencies match the payment frequencies.)

What variable would you solve for to find the monthly savings contribution? a. Present value b. Payment c. Interest rate d. Time e. Future Value

What is the monthly savings contribution you must make to fully fund your retirement?

Answer 1

1). Payment is the variable that tells us the monthly contribution. So, Option "B" is correct.

Present Value is the variable that tells us the present value of the monthly contribution.

Interest rate is the variable that tells us the rate earned on the monthly contribution.

Time is the variable that tells us the number of the monthly contributions to be made.

Future Value is the variable that tells us the future value of the monthly contribution.

2). To find the monthly savings contribution you must make to fully fund your retirement, we need to find the amount needed at retirement.

PVA = Annuity x [{1 - (1 + r)^-n} / r]

= $7,500 x [{1 - (1 + 0.035/12)^-(35*12)} / (0.035/12)]

= $7,500 x [0.7057 / 0.0029] = $7,500 x 241.96 = $1,814,703.60

So, this is the fund needed at the retirement, Now we can treat this as the Future Value of the monthly savings contribution. So,

Monthly Savings Contribution = [FVA x r] / [(1 + r)ⁿ - 1]

= [$1,814,703.60 x (0.066/12)] / [{1 + (0.066/12)}^(40*12) - 1]

= $9,980.87 / 12.9122 = $772.98