Question

You open a money market account with $7500 at 5% compound quarterly. After two years, $1500 is withdrawn from the account to buy a new computer. A year later, $2000 is put in the account. What will be the ending balance if the money is kept in the account for another three years?

Answer 1

$10,596.81

Explanation:

The balance on an account earning 5% interest compounded quarterly can be found using the formula ...

A = P(1 +0.05/4)^(4t)

where P is the principal invested and t is the number of years.

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Here, we are investing $7500.00. After 2 years, the account balance will be ...

A = $7500(1 +0.05/4)^(4·2) = $8283.65

After the $1500 withdrawal, the new balance will be ...

$8583.65 -1500.00 = $6783.65

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This is the amount earning interest for the next year, after which time the balance will be ...

A = $6783.65·(1.0125)^(4·1) = $7129.24

When $2000 is added to the account, the principal earning interest for the last 3 years is ...

$7129.24 +2000.00 = $9129.24

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The final balance after 3 more years is then ...

A = $9129.24·(1.0125)^(4·3) = $10,596.81

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These calculations are conveniently carried out by a spreadsheet, as in the attached. Since the account changes are all done at the end of the year, we don't have to keep track of the quarterly balances. The formula used to calculate the ending balance each year is shown.