Question

Individual A just turned 30 years old, have just received your MBA, and have accepted your first job. He must decide how much money to put into its retirement plan. The plan works as follows: Every dollar in the plan earns 7% per year. You cannot make withdrawals until he retires on his sixty-fifth birthday. After that point, individual A can make withdrawals as he sees fit.

Individual A decides that he will plan to live to 100 and work until hi turns 65. He estimates that to live comfortably in retirement, he'll need $100,000 per year starting at the end of the first year of retirement and ending on his one-hundredth birthday.

Individual A will contribute the same amount to the plan at the end of every year that you work.

(a) How much does Individual A need to contribute each year to fund his retirement? The situation above is not very realistic because most retirement plans do not allow you to specify a fixed amount to contribute every year. Instead, you are required to specify a fixed percentage of your salary that you want to contribute. Assume that your starting salary is $75,000 per year and it will grow 2% per year until you retire.

(b) Assuming everything else stays the same as in the previous question, what percentage of his income does he need to contribute to the plan every year to fund the same retirement income?

Answer 1

First, we calculate the PV of retirement corpus
P = PMT x (((1-(1 + r) ^- n)) / r)
Where:
P = the present value of an annuity stream	To be calculated
PMT = the dollar amount of each annuity payment	100000
r = the effective interest rate (also known as the discount rate)	7%
n = the number of periods in which payments will be made	35
PV of annual withdrawl from retirement corpus=	PMT x (((1-(1 + r) ^- n)) / r)
PV of annual withdrawl from retirement corpus=	100000* (((1-(1 + 7%) ^- 35)) / 7%)
PV of annual withdrawl from retirement corpus=	$       1,294,767
This fund has to be built with contributions
FV of annuity
P = PMT x ((((1 + r) ^ n) - 1) / r)
Where:
P = the future value of an annuity stream	$       1,294,767
PMT = the dollar amount of each annuity payment	To be computed
r = the effective interest rate (also known as the discount rate)	7%
n = the number of periods in which payments will be made	35
1294767=	PMT * ((((1 + 7%) ^ 35) - 1) / 7%)
1294767=	PMT * 138.236
Annual deposit=	1294767.23/138.236
Annual deposit=	$              9,366
If the fixed percentage will be contributed, then the annual contribution will also increase at par with a salary so 2% growing contribution
FV of a growing annuity
P = PMT x (((1 + r)^n-(1+g)^n)/(r-g))
Where:
P = the future value of an annuity stream	$       1,294,767
PMT = the dollar amount of each annuity payment	To be computed
r = the effective interest rate (also known as the discount rate)	7%
n = the number of periods in which payments will be made	35
g= Annual growth	2%
1294767=	PMT x (((1 + r)^n-(1+g)^n)/(r-g))
1294767=	PMT * (((1 + 7%)^35-(1+2%)^35)/(7%-2%))
1294767=	PMT * 173.5338
First contribution=	1294767.23/173.5338
First contribution=	7,461.18
First Salary	75000
Fixed contribution percentage=	7461.18/75000
Fixed contribution percentage=	9.95%