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

Question

Beck

Business

29 May, 04:55

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

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Answers (1)

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Kian Sampson · Answer 1

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