Question

Suppose that you just turned 25 years old and that you wish to receive an annual annuity of $76,697 for 30 years (end of each year age 65-95). How much would you have to contribute annually at the end of each year ages 25-60 , if you then let the funds vest until age 65 with no further contributions? Your EAR is 5.2%.

Answer 1

Present Value of Annuity required at 65 =

where r is the rate of Return for compounding period = 5.2%

n is the no of compounding period 30 years

=

= 1152610.74137

Now present Value 1152610.74137 will be required at the age of 60 (5 years earlier the age of retirement)

Present Value required at 60 = 1152610.74137 / (1+r)^n

r = 0.052

n = 5 years

= 1152610.74137 / (1+0.052)^5

= 894,548.64751

Now. this 894,548.64751 will be the Future Value required from todays prespective.

Future Value Annuity =

r = 0.052

n = 35 (from age 24 to age 60)

894,548.64751 =

894,548.64751 = Periodic Payment * 94.1521279461

Periodic Payment = 894,548.64751 / 94.1521279461

Periodic Payment =$9501.10