5 Find the final amount in the following retirement account

5) Find the final amount in the following retirement account, in which the rate of return on the account and the regular contribution change over time. $509 per month invested at 5%, compounded monthly, for 4 years; then $782 per month invested at 77%, compounded monthly, for 4 years. What is the amount in the account after 8 years? $ (Round to the nearest dollar as needed.)

Solution

For 1st 4 years : FV = PMT[ (1+i)^n - 1]/i

PMT = $ 509 ; i = 0.05/12 =0.004167 ; n =5*12 = 60

FV = 509[ 1.004167^60 -1]/0.004167

= $ 34615.45

For 4 yrs ; i = 0.077/12 = ; n = 4*12 = 48

FV = 782[ (1.00641^48 -1)/0.00641

= 782*0.359/0.00641

= $ 43796.88

Total amount = $ 43796.88 + $ 34615.45

= $ 78412.33

= $78412