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

Amount John want to have at age 55,

$2,000*12*15=360,000$

currently he wants to invest 10,000

find the future value of the 10,000

$future \, value=present \,value * (1+r )^n$

$future \, value=10,000 * (1+0.05)^{360}$

$future \, value=60,225,$

$360,000-60,225=299,775$

John's monthly savings would total to 299,775 at the age of 55

$future \, value \, of \, annuity= present \, value *\frac{1-(1+r )^{-n}}{r}$

$299,775 = x *\frac{1-(1+0.005 )^{-360}}{0.005}$

$x=montly \, deposit$

$John's \, monthly \, deposit=1,797$