Question

You have just turned 30 years old, have just received your MBA, and have accepted your first job. Now you must decide how much money to put into your retirement plan. You are required to specify a fixed percentage of your salary that you want to contribute. Assume that your starting salary is $ 74 000 per year and it will grow 2.1 % per year until you retire. Every dollar in the plan earns 7.4 % per year. You cannot make withdrawals until you retire on your sixty-fifth birthday. After that point, you can make withdrawals as you see fit. You decide that you will plan to live to 100 and work until you turn 65. You estimate that to live comfortably in retirement, you will need $ 97 000 per year starting at the end of the first year of retirement and ending on your 100th birthday. What percentage of your income do you need to contribute to the plan every year to fund your retirement income?

the fraction of your salary you should save is: _ %.

Answer 1

Size of the kitty at the time of retirement, = Such an amount that should enable an annual payment of $ 97,000 for the next 100 - 65 = 35 years.

Interest rate= 7.4%

We make use of excel function here. We have to find the PV of the kitty at the time of retirement that would result in to a

PMT = - $ 97,000

Rate = 7.4%

Period = 35 years

Hence, PV = (Rate, period, PMT) = PV(7.4%, 35, -97000) = $1,203,067.54

This is the size of kitty required at t=65

This size of kitty is nothing but future value of a growing annuity over t = 30 to t=65 i,e over a period of 65 - 30 = 35 years

Interest rate, i = 7.4%

Growth rate in annuity = g = 2.1%

Let's assume A is the first payment ie contribution from the first salary.

The formula for FV of an annuity A, growing at "g" and earning interest rate of 'i" over "n" period is:

$FV=A\times \frac{(1+i)^{n} - (1+g)^n}{i-g}$

$1203067.54=A\times \frac{(1+0.074)^{35} - (1+0.021)^{35}}{0.074-0.021} = 190.50\times A$

hence, A = $1,203,067.54 / 190.50 =  6,315.39

Hence, the desired fraction of salary =  6,315.39 / 74,000 = 8.53%