Question

Irene plans to retire on January 1, 2020. She has been preparing to retire by making annual deposits, starting on January 1, 1980, of 2100 dollars into an account that pays an effective rate of interest of 7.2 percent. She has continued this practice every year through January 1, 2001. Her goal is to have 1.35 million dollars saved up at the time of her retirement. How large should her annual deposits be (from January 1, 2002 until January 1, 2020) so that she can reach her goal?

Answer 1

Years from Jan 1, 1980 to Jan 1, 2001 (n)= 21

Annual deposit (P)= 2100 dollars

Interest rate (i) = 7.2%

Value as onn Jan 1, 2001 (future value of annuity formula) = P*(((1+i)^n)-1)/i

=2100*(((1+7.2%)^21)-1)/7.2%

=96429.76211

This is single present value amount accumulated on jan 1, 2001 = 96429.76211

Number of years from jan 1, 2001 to jan 1, 2020 (n) =19

Future value of present value = Present value*(1+i)^n

=96429.76211*(1+7.2%)^19

=361336.6528

This is future value of deposits made upto now on Jan 1, 2020 =361336.6528

Required amount accumulation at retirement =1350000

Remaining future value required =1350000-361336.6528 = 988663.3472

Number of years for deposit (n) = 19

interest rate(i) = 7.2%

Annuity amount or Amount required to save each year Formula = Future value*i/(((1+i)^n)-1)

988663.3472*7.2%/(((1+7.2%)^19)-1)

=25911.87086

So we required to save $25911.87 each year to meet our goal.