Answer to Question #120811 in Financial Math for Matelita Sinukula

Question

John is currently 25 years.He has $10000 saved up and wishes to deposit this into his 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

Solution

Monthly interest rate = (0.06/12) = 0.005

To withdraw $2,000 every month for 15 years after retirement:

PMT = $2,000

N = (15*12) = 180

i=0.005

PV = PMT / i(1-(1+i)^-n)

PV = 2000/0.005(1-(1+0.005)^-180) = 237,007.03

Amount required at age 55 = $237,007.03 (Future value for savings account started at age 25 till age 55)

For savings account:

PMT = $X

N=(30*12) = 360

i=0.005

FV=$237,007.03

P=$10,000

FV = P(1+i)ⁿ + PMT/i[(1+i)ⁿ – 1]

237,007.03 = 10,000(1+0.005)³⁶⁰ + x/0.005[(1+0.005)³⁶⁰ – 1]

237,007.03 = 60,225.75 + x/0.005[5.0226]

X(1004.52) = 176,781.278

X = 175.98669 ~ 175.99

Monthly deposit = 175.98669 ~ $175.987