Question

Suppose that you decide to start putting money into an annuity each month. Suppose further that the annuity pays 4.8% interest compounded monthly. If you begin paying in at age 21, what would your annuity be worth at age 65?

a. Leave P as a variable and use the annuity fprmula to solve for the value of the annuity when you are 65 in terms of P.

b.If you put $50 into this annuity every mont, how much will it be worth when you turn 65?

c. How much money will you put into the annuity in total by the time you turn 65? (HINT: Multiply the value of the monthly investment by the number of investments you would need to make.)

d. Suppose you instead wanted to invest all at once in a continuously compunded certificate of deposit with the same interest rate and time period. How much would you needed to put in up-front to have the same amount you got fromthe annuity when you turn 65?

Answer 1

a. Answer is 1,814 x P

Future value of an annuity P which starts now is

FV = (1+r) x P x (((1+r)^n-1))/r)

where P is the annuity, r = 4.8/12 = 0.4% and n = 528 -- (65-21)x12

FV = (1+0.004) x P x (((1+0.004)^528 - 1)/0.004)

= 1.004 x P x (8.23001-1)/0.004) = 1.004 x P X 1807.50 = 1,815 x P (rounded)

b. Answer is $ 90,750 (1,815 x 50).

c. Total money put into the annuity = $26,400 (528 x $50)

d. Answer is $11,207

Working:

Future value of a sum invested @4.8% compounded monthly for 44 years is

P x (1+0.004)^528

This should be equal to $90,750

P x (1.004)^528 = 90,750

P = 90,750 / 8.23001 = $11,027