Question

# James Smith is 30 years and wants to retire when he is 65. So far he...

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.)

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

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