The Design Team just decided to save $1,500 a month for the next 5 years as a safety net for recessionary periods. The money will be set aside in a separate savings account which pays 4.5 percent interest compounded monthly. The first deposit will be made today. What would today's deposit amount have to be if the firm opted for one lump sum deposit today that would yield the same amount of savings as the monthly deposits after 5 years?

Question

Business

Prego

30 April, 00:40

The Design Team just decided to save $1,500 a month for the next 5 years as a safety net for recessionary periods. The money will be set aside in a separate savings account which pays 4.5 percent interest compounded monthly. The first deposit will be made today. What would today's deposit amount have to be if the firm opted for one lump sum deposit today that would yield the same amount of savings as the monthly deposits after 5 years?

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Answers (1)

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Tiana Mason · Answer 1

Lump sum required = $80,459.07

Explanation:

Giving the following information:

Monthly deposit = $1,500

Number of months = 5*12 = 60

Monthly interest rate = 0.045/12 = 0.00375

First, we need to calculate the final value of the monthly deposit. We will use the following formula:

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

A = monthly deposit

FV = {1,500*[ (1.00375^60) - 1]} / 0.00375

FV = $100,718.33

Now, we need to determine the lump sum required:

PV = FV / (1+i) ^n

PV = 100,718.33 / (1.00375^60)

PV = $80,459.07