Answer:
$985.92
Step-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 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
[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 quarters
i=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.
