MATH SOLVE

4 months ago

Q:
# Meg's pension plan is an annuity with a guaranteed return of 7% per year (compounded quarterly). She would like to retire with a pension of $10,000 per quarter for 10 years. If she works 26 years before retiring, how much money must she and her employer deposit each quarter? HINT [See Example 5.] (Round your answer to the nearest cent.)

Accepted Solution

A:

Answer:$985.92Step-by-step explanation:In order to solve this question, we are going to use two formulas.Present Value of an Annuity[tex]PV=PMT\frac{1-(1+i)^{-n} }{i}[/tex]To get the value of the pension of 10,000 per quarter for 10 years. And Sinking funds Payments Formula[tex]PMT=FV\frac{i}{(1+i)^{n}-1}[/tex]to get the Payment to be deposited each quarter during 26 years.So for the first formulan= number of periods = we need to know how many quarters in 10 years are. We know there are 4 quarters in a year, so 10 years multiplied by 4 is 40 quartersn= 40For i=interest rate= it is 7% compounded quarterly. There are 4 quarters so we divide by 4 and we get: i=7%/4=1,75%PMT= 10,000[tex]PV=10,000\frac{1-(1+0.0175)^{-40} }{0.0175}\\\\PV=$285,942.30[/tex]and these 285,942.30 would be our future value in the sinking fund payment formula with:n= 26 years *(4 quarters a year)= 104 quartersi=1.75%FV=$285,942.30[tex]PMT=FV\frac{i}{(1+i)^{n}-1}\\\\PMT=285,942.30\frac{0.0175}{(1+0.0175)^{104}-1}\\\\PMT=985.92[/tex]And $985.92 would have to be deposited every quarter during 26 years to get a payment of $10,000 per quarter for 10 years.