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.)

$985.92

Step-by-step explanation:

In order to solve this question, we are going to use two formulas.

Present Value of an Annuity

To get the value of the pension of 10,000 per quarter for 10 years. And

Sinking funds Payments Formula

to get the Payment to be deposited each quarter during 26 years.

So for the first formula

n= 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 quarters

n= 40

For 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

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 quarters

i=1.75%

FV=$285,942.30

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.