Question

John is currently 25 years old. He has $10,000 saved up and wishes to deposit this into a savings account which pays him J12 = 6% p.a. He also wishes to deposit $X every month into that account so that when he retires at 55, he can withdraw $2000 every month end to support his retirement. He expects to live up till 70 years. How much should he deposit every month into his account?

Answer 1

Sol:

PMT = $2000

Interest rate (r) = 6% p.a (Monthly) = 6%/12 = 0.5%

Period (n) = 15 years (Monthly) = 15 x 12 = 180 (Withdrawal of $2000 every year after age 55 till age 70 = 15 years)

Present value (PV) = PMT/r (1-(1+r)^-n

PV = $2000/0.5% (1-(1+0.5%)^-180

PV =$2000/0.005 (1-(1.005)^-180

PV = $400,000 / 0.5925 = $237,007.03

Therefore amount needed at the age of 55 to withdraw $2000 every month till age 70 is = $237,007.03.

Now future value (FV) of amount deposited from age 25 till 55 in his saving account will be $237,007.03

Principal (P) = $10,000

PMT = $X

Interest rate (r) = 6% p.a (Monthly) = 6%/12 = 0.5%

Period (n) = 30 years (Monthly) = 30 x 12 = 360

FV = P (1+r)^n + PMT/r(1+r)^n - 1

237,007.03 = 10,000 (1+0.5%)^360 + X/0.5%(1+0.5%)^360 - 1

237,007.03 = 10,000 (1.005)^360 + X/0.005(1.005)^360 - 1

237,007.03 = 60,225.75 + X/0.005(5.0226)

X(5.0226 / 0.005) = 237,007.03 - 60,225.75

X(1,004.52) = 176,781.28

X = 176,781.28 / 1,004.52 = $175.99

Therefore the amount he deposit every month into his account is $175.99