Question

Claudia deposited $3,000 into a savings account that earns 4% interest compounded annually. Part of Claudia's bank statement isshown. How much interest does she earn in Year 3? Round to the nearest cent.

Answer 1

She earns $129.79 interest in Year 3.

Explanation:

The compound interest formula is given by:

`A(t) = P(1 + (r)/(n))^(nt)`

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit year and t is the time in years for which the money is invested or borrowed.

In this question, we have that:

`P = 3000, r = 0.04, n = 1`

How much interest does she earn in Year 3?

Her amount after the first year is A(1).

Her amount after the second year is A(2).

Her amount after the third year is A(3).

A(1) is the initial amount plus what she earns in interest during year 1.

A(2) is A(1) plus what she earns in interest during year 2.

A(3) is A(2) plus what she earns in interest during year 3.

So the interest that she earns in Year 3 is A(3) - A(2).

In which

`A(t) = P(1 + (r)/(n))^(nt)`

`A(2) = 3000(1 + (0.04)/(1))^(2) = 3244.8`

`A(3) = 3000(1 + (0.04)/(1))^(3) = 3374.59`

`A(3) - A(2) = 3374.59 - 3244.8 = 129.79`

She earns $129.79 interest in Year 3.