Question

With wages from a summer job you make a total of 13 deposits at $962 per month into a savings account earning 6.19% compounded monthly. At the time of the last deposit, you close the savings account and invest all the money in stocks with the intention of leaving the stocks alone for the subsequent 16 years (dividends automatically are reinvested). The stocks are expected to provide an average annual return of 16.39% compounded monthly. When you finally sell the stocks, how much do you get?

Answer 1

First we have to find the accumulated value after13 deposits which are the monthly.Use FV function in EXCEL

=FV(rate,nper,pmt,pv,type)

rate=6.19%/12=0.5158%

nper=number of periods=13

pmt=deposits=962

pv=0

type=0 (deposits are made at the end of the month)

=FV(0.5158%,13,-962,0,0)

FV=$12,900.48

This amount is transferred to share market at 16.39% compounding monthly for 16 years. Use FV formula

Future value=Present value*(1+(r/n))^(n*y)

Present value=12,900.48

n=12 months

y=number of years=16

r/n=16.39%/12=1.3658%

n*y=12*16=192

Future value=12900.48*((1+1.3658%)^192)=12900.48*13.5265=$174,498.63

The total amount you get after selling the stocks=$174,498.63