Question

Derek will deposit $4,355.00 per year for 30.00 years into an account that earns 9.00%, The first deposit is made next year. How much will be in the account 45.00 years from today?

Answer 1

Future value of $4355 Deposted each year at 9% after 30 years is given by=

=($4355(1+9%)^29+$4355(1+9%)^28+$4355(1+9%)^27+.............+$4355(1+9%)^3+$4355(1+9%)^2+$4355(1+9%)^1)+$4355(1+9%)^0

=$4355* Annuity Factor(9%,29 years )+$4355

=4355*135.3075+4355

=589264.33+4355= $ 593619.33

Amount after 45 years is given by = Amount after 30 years (1+ 9%)^(45-30)years

=$593619.33*(1+9%)^15

= $593619.33* 3.642482

=$2162248

Hence amount after 45 years will be $2162248

(Note: Since the first payment will be made after 1 year hence time remaining for the purpose of compounding in 30 years will 29 years for first deposit and 28 years for next deposit and so on . hence the year used in compounding of first payment in 30 years calculation is taken as 29 and so on. And the last deposit will be made at the end of 30 years hence there wont be any compounding while computing the value at the end of 30 years)