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 2000 dollars into an account that pays an effective rate of interest of 9.9 percent. She has continued this practice every year through January 1, 2001. Her goal is to have 1.5 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 in Dollars please

Answer 1

Let us calculate future value as on jan1 2001

No of annual deposits is 21 amount is 2000 rate of interest is 9.9%

Future value is 2000(FVIFA 9.9% 21Y)

= 2000(63.48) = 126960

F.v as on 2020 is 126960(1.099)^19 = 763173

Target amount is 1500000

Excess amount needed is 736826

This is annuity where periodic payments are made at the end of period

Formula

Future value of annuity is

P((1+r)^n -1)/r

Where p is periodic payment

R is rate per period

N is no of periods

736826 = p((1.099)^19 -1)0.099

736826 = p (50.617)

Periodic payment is 14557