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:
[tex]FV=PMT\frac{(1+\frac{r}{n} )}{\frac{r}{n} } ^{n*t}[/tex]
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:
[tex]FV=300\frac{(1+\frac{0.07}{12} )}{\frac{0.07}{12} } ^{12*40}[/tex]
[tex]300*\frac{(1.005833)^{480}}{0.005833} =300* 2,795.96[/tex]
∴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
