Question

1. For 20 years Jenny deposits $500 at the end of each month in an account earning 4.5% per year compounded monthly.
   1. How much will she have in the account in 20 years?
   2. How much interest did she earn in this 20 year period?
   3. for the next 25 years Jenny neither deposits nor withdraws any money while the account continues to earn 4.5% per year compounded monthly.
      1. How much does Jenny have in the account after these 25 years?
      2. How much interest did she earn in this 25 year period?
      3. What equal amounts would she have had to deposit in the account at the end of each month for all 45 years in order to achieve the same result as in a.)?

Answer 1

1. a.The formula is FV function in EXCEL

It si compounded monthly,

=FV(rate,nper,pmt,fv,0)

=FV((4.5%/12),240,-500,0,0)

FV=$194,062.18

The amount becomes $192,062.18 in 20 years

b. deposits made in 20 years=240*500=$120,000

Interest earned in 20 years=$194,062.18-$120,000=$74,062.18

c. In next 25 years, the amount becomes=$194.062.18*(1+(4.5%/12))^(25*12)

=$194.062.18*(3.073743)=$596,497.18

2.a. If it is for 25 years,

then FV=((4.5%/12),300,-500,0,0)

FV=$276,499

b.Deposits made=$500*300=$150,000

Interest earned=$276,499-$150,000=$126,499

c. To earn $276,499 in 45 years, we should make monthly deposits. We can find using PMT function in EXCEL

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

nper=45*12=540

pv=0

fv=$276,499

=PMT((4.5%/12),540,0,276499,0)

PMT=$158.36

He has to deposit $158.36 in every month for next 45 years to accumulate $276,499