Question

James Smith is 30 years and wants to retire when he is 65. So far he has saved (1) $5,000 in an IRA account in which his money is earning 8.3 percent annually and (2) $4,000 in a money market account in which he is earning 5.25 percent annually. James wants to have $1 million when he retires. Starting next year, he plans to invest the same amount of money every year until he retires in a mutual fund in which he expects to earn 7.00 percent annually. How much will James have to invest every year to achieve his savings goal? (Round answer to 2 decimal places, e.g. 15.25.)

Answer 1

Let us calculate the future values of individual investments

Future value of IRA=FW1=5000*(F/P,0.083,35)

We know that (F/P,0.083,25)=(1+0.083)^35=16.292810

So, FW1=5000*16.292810=$81464.05

Future value of investment in money market=FW2=4000*(F/P,0.0525,35)

We know that (F/P,0.0525,35)=(1+0.0525)^35=5.994786

So, FW2=4000*5.994786=$23979.14

Let he invests amount X per year mutual fund,

Future value of mutual fund investment=FW3=X*(F/A,0.07,35)

We know that

So, FW3=X*(F/A,0.07,35)=138.236878X

We know that

FW1+FW2+FW3=1000000

81464.05+23979.14+138.236878X=1000000

X=(1000000-81464.05-23979.14)/138.236878=$6471.19