Question

Suppose that you just turned 25, plan to retire at 65, and estimate that you will need $9,471 per month at the end of each month upon retirement for the next 30 years. How much do you need to contribute at the end of each month until you reach age 50? Assume your estimated return is 6.2% EAR, that you have $10,000 already invested, and the funds will continue to earn interest to age 65, even though you will not continue contributing after age 50.

Answer 1

ANSWER DOWN BELOW. FEEL FREE TO ASK ANY DOUBTS. THUMBS UP PLEASE.

Formula: The present value of an ordinary annuity (PV)

PV = C× [1-(1+r)^-n]/r

PV = Present value (The cummulative amount available at Present)

C= Periodic cash flow. 9471

r =effective interest rate for the period. (1+6.2%)^(1/12)-1 = 0.5025% = 0.005025

n = number of periods. 30*12 = 360

PV = 9471× [1-(1+0.005025)^-360]/0.005025

PV = $1,574,530.91. (Amount required at age 65)

Formula:

Future value= present value(1+r)^n

r= interest rate for the period.

n = number of periods.

$1,574,530.91 = PV*(1.062)^15

PV = $638,680.18 (amount required at age 50).

Formula: The Future Value of an ordinary annuity (FV)

FV= C× {[(1+r)^n]-1}/r

FV = Future value (The cumulative amount available in Future at age 50) $638,680.18

C= Periodic cash outflow. ?

r =effective interest rate for the period. 0.005025

n = number of periods. 25*12 =300

$638,680.18= C× {[(1+0.005025)^300]-1}/0.005025 + 10,000*(1.06)^25

C= $852.69

Amount to be contributed each month until the age of 50 is $852.69