Answer to Question #119832 in Financial Math for Sela

Question

III. 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? (10 Marks)

Answer 1

First we work out John's retirement plan;

Which is to have 2,000/ every month for 15 years.

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

$$future value = present value *( 1+r)\left(^{\smash{n}}\right)$$

$future value = 10,000 *( 1+0.005)\left(^{\smash{360}}\right)$

$future value=60,225.75$

$Amount to invest=360,000-60,225.75$

$Amount to invest=299,774.25$

$Amount to Invest= monthly payment *{1-(1+r )\left(^{\smash{n}}\right) \above{2pt} r}$

$Amount to Invest= monthly payment *{1-(1+0.005 )\left(^{\smash{-360}}\right) \above{2pt} 0.005}$

$299,774.25= x *{1-(1+0.005 )\left(^{\smash{-360}}\right) \above{2pt} 0.005}$

$x=1,797.30$

$Monthly Deposit=1,797.30/$