You just opened a brokerage account, depositing $3,500. You expect the account to earn an interest rate of 9.652%. You also plan on depositing $4,500 at the end of years 5 through 10. What will be the value of the account at the end of 20 years, assuming you earn your expected rate of return?

$108,583.98

Explanation:

Given:

Initial deposit = $3,500

Rate = 9.652%

You also plan on depositing $4,500 at the end of years 5 through 10.

Required:

What will be the value of the account at the end of 20 years, assuming you earn your expected rate of return?

First calculate the future value of first installment, $3500 at end of year 20, since the amount was not deposited at once:

Calculate the future value of annual deposits at end of year 10:

Given, N = 6 years )i.e from 5 to 10 years)

I/Y = 9.652%

PV = 0

PMT = $4,500

FV(9.652%, 6, 4500, 0)

FV = $34,416.63

Calculate the future value of annual deposits at end of year 20:

Given, N = 10 Years (from end of year 10, to year 20)

PV = 34,416.43

I/Y = 9.652%

FV = 34,416.43 * PVIF(0.9652, 10)

FV = $86,483.63

The total future value at end of year 20:

Future value of initial deposit + Future Value of annual deposits

= $22,100.35 + $86,483.63

= $108,583.98

The value of the account at the end of 20 years = $108,583.98

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