Donald Martin is 30 years and wants to retire when he is 65. So far he has saved (1) $6,450 in an IRA account in which his money is earning 8.3 percent annually and (2) $4,300 in a money market account in which he is earning 5.25 percent annually. Donald 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 8.54 percent annually. How much will Donald have to invest every year to achieve his savings goal

Annual deposit = $4,169.59754

Explanation:

Giving the following information:

Donald Martin is 30 years and wants to retire when he is 65.

PV = 6,450 + 4,300 = $10,750

i = 0.0854

Number of years = 35

First, we need to calculate the final value of the initial investment:

FV = PV * (1+i) ^n

FV = 10,750 * (1.0854^35)

FV = 189,257.05

Now, we can calculate the annual deposit required. We need to use the following formula:

FV = {A*[ (1+i) ^n-1]}/i

A = annual deposit

Isolating A:

A = (FV*i) / {[ (1+i) ^n]-1}

FV = 1,000,000 - 189,257.05 = 810,742.95

A = (810,742.95*0.0854) / [ (1.0854^35) - 1]

A = $4,169.59754