How much must be deposited at the beginning of each year in an account that pays 4%, compounded annually, so that the account will contain $36,000 at the end of 9 years? (Round your answer to the nearest cent.)

Question

Business

Alannah Robertson

28 March, 14:49

How much must be deposited at the beginning of each year in an account that pays 4%, compounded annually, so that the account will contain $36,000 at the end of 9 years? (Round your answer to the nearest cent.)

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Answers (1)

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Fabian · Answer 1

Annual deposit = $3,270.91

Explanation:

Giving the following information:

Deposit = beginning of the year

Interest rate = 4% compounded annually

Final value = $36,000

Number of years = 9

To calculate the annual deposit, we need to use the following formula:

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

A = annual deposit

Isolating A:

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

A = { (36,000*0.04) / [ (1.04^9) - 1]} / 1.04

A = $3,270.91