Question

not using excel plz

Problem 7 Jamal Brown is a 55-year-old engineer. According to mortality tables, a male at age 55 has an average life expectancy of 21 more years. Jamael has accu- mulated $200,000 toward his retirement. He is now

Answer 1

At current time, the investors age is 55. Provisions need to be made up to an age of 76. Savings + Withdrawal Tenure = (76-55) = 21 years

Savings Interest Rate = 5 %, Annual Savings Amount = $ 10000, Initial Savings at age 55 = $ 200000, Target Annual Retirement Withdrawals = $ 100000

Let the savings tenure be n years beginning at age 55. Hence, retirement age = 55 + n

Therefore, Withdrawal Tenure = 76 - 55 - n = 21 - n years

As per the principles of time value of money, we have: 200000 x (1.05)^(n) + 10000 x [{(1.05)^(n)-1}/{(1.05)-1}] = 100000 x (1/0.05) x [1-{1/(1.05)^(21-n)}]

Using Excel's Goal Seek Function to solve the above equation, we get: n = 13.876 years ~ 14 years

Hence, the additional savings period is 14 years beginning at age 65 whereas the withdrawal tenure is (21-14) = 7 years