Question

7

7. Suppose you buy your home when you are 35, and so it will be paid off by the time you are 65, when you retire. It would be wise to save enough money to take monthly payouts until you are age 90 Older people who no longer have an income often move their investments to a more secure, lower-interest option because these investments are less likely to crash or suddenly lose all their value. Suppose you move your annuity from the 4% rate you had been earning while you were ages 35- 65 to a safer annuity earning 2.96% (the highest guaranteed long-term annuity rate) during the ages from 65-90. It is from this safer annuity that you will take monthly payouts. How much will you have to put into your monthly annuity earning 4% from the age of 35 to the age of 65 if you wish to receive monthly payouts of a. $3000? b. $5000? c. $8000?

Answer 1

(a) Pre-Retirement Interest Rate = 4 % or (4/12) = 0.33 % per month and Post-Retirement Interest Rate = 2.96 % or (2.96/12) = 0.2467 %

Savings Tenure = 65-35 = 30 years and withdrawal Tenure = 90 - 65 = 25 years

Required Monthly Withdrawals = $ 3000

Present Value of Withdrawals at age 65 = PV(65) = 3000 x (1/0.002467) x [1-{1/(1.002467)^(300)}] = $ 635385.64

Let the required monthly savings be $ p

Therefore, p x (1.0033)^(359) + p x (1.0033)^(358) +....................+ p = 635385.64

p x [{(1.0033)^(360)-1}/{(1.0033)-1}] = 635385.64

p x 689.12228 = 635385.64

p = $ 922.022

(b) Required Monthly Withdrawals = $ 5000

PV(65) = 5000 x (1/0.002467) x [1-{1/(1.002467)^(300)}] = $ 1058976.064

Let the required monthly deposits be $ k

Therefore, k x (1.0033)^(359) + k x (1.0033)^(358) +...........+ k = 1058976.064

k x 689.12228 = 1058976.064

k = 1058976.064 / 689.12228 = $ 1536.703

(c) Required Monthly Withdrawals = $ 8000

PV(65) = 8000 x (1/0.002467) x [1-{1/(1.002467)^(300)}] = $ 1694361.703

Let the required monthly deposits be $ m

Therefore, m x (1.0033)^(359) + m x (1.0033)^(358) +.............+ m = 1694361.703

m x 689.12228 = 1694361.703

m = 1694361.703 / 689.12228 = $ 2458.725