Question

Jennifer's pension plan is an annuity with a guaranteed return of 7% per year (compounded monthly). She can afford to put $300 per month into the fund, and she will work for 40 years before retiring. If her pension is then paid out monthly based on a 20-year payout, how much will she receive per month

Answer 1

Answer:

She will receive $3,494.95 per month.

Explanation:

Jennifer's pension plan is an example of a sinking fund.

A sinking fund is an account that earns compound interests and into which periodic payments are also made.

The formula for calculating the future value of payments in a sinking fund account is given as:

$FV=PMT\frac{(1+\frac{r}{n} )}{\frac{r}{n} } ^{n*t}$

where:

FV = Future value

PMT = periodic payment = $300

r = interest rate in decimal = 7% = 0.07

n = compounding period per year = monthly = 12

t = number of years compounded = 40

hence:

$FV=300\frac{(1+\frac{0.07}{12} )}{\frac{0.07}{12} } ^{12*40}$

$300*\frac{(1.005833)^{480}}{0.005833} =300* 2,795.96$

∴FV = $838,786.8

Finally, we are asked to calculate the amount she will be paid per month in a 20-year payout period, and this is shown below:

20 years = 12 months × 20 = 240 months

Therefore, amount to be paid in a 240 month period =

future value ÷ total number of months 838,786.8 ÷ 240 = $3,494.95