Question

On your birthday, when you turned 24, $25400 was deposited in an account which earns 10.5% compounded annually.

a.  How much can you withdraw annually for 11 years if the first withdrawal is made on the day you become 49?

b.  State the total amount of interest earned on this account.

Answer 1

We have to find the future value of the deposit for the next 25 years (from 24 to 49)

Future value=Present value*(1+interest rate)^n

interest rate=10.5%

n=25

Accumulated value after 25 years=$25,400*((1+10.5%)^25)=$308,241.2

The interest earned in first part=$308,241.2-$25,400=$282,841.2

a. ==> For annual withdrawals, use PMT function in EXCEL

=PMT(rate,nper,pv,fv,type)

rate=10.5%

nper=number of years=11

pv=$308,241.2

fv=0

type=1 (because withdrawls happens in the begining of the each year)

=PMT(10.5%,11,-308,241.2,0,1)

PMT=Annual withdrawls=$43,941.72

In second part the total interest earned=(11*$43,941.72)-$308,241.2=$483,358.9-$308,241.2=$175,117.7

b. Find the total interest earned by adding $282,841.2+$175,117.7=$457,958.93