# How much interest did she earn? (compound interest)

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Anne inherited some money from her grandfather and put it in a bank account that earns 10% interest compounded quarterly. After 4 years, Anne had $600.00 in the bank account. How much interest did she earn? (ROUND TO THE NEAREST CENT)

Anne inherited some money from her grandfather and put it in a bank account that earns 10% interest compounded quarterly. After 4 years, Anne had $600.00 in the bank account. How much interest did she earn? (ROUND TO THE NEAREST CENT)

##### 2 Answers

Total Interest of 4 years is:

#### Explanation:

Given:

Annual compound interest is 10%

Calculation cycle: 4 times a year.

Final sum in account: $600.00 after 4 years.

Let the initial unknown principle sum be

Let the total interest in dollars be

Let the count of years be

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As the is a cycle of 4 calculations per year we have the indices of

This is over 4 years so

Rounding gives:

Thus the interest is the difference.

#### Explanation:

Compound interest is given by the formula:

Where:

We are give interest rate of

compounding period is quarterly so,

Time period is 4 years so:

To find the amount of interest earned, we first need to find the present value:

Using:

Interest earned is: