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**

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