To calculate the amount earned with simple interest, you can use the formula:
\[ A = P(1 + rt) \]
where:
- \(A\) is the amount of money accumulated after \(t\) years, including interest.
- \(P\) is the principal amount (the initial amount of money).
- \(r\) is the annual interest rate (in decimal).
- \(t\) is the time the money is invested or borrowed for, in years.
In this case:
- \(P = 800\)
- \(r = 0.15\) (15% expressed as a decimal)
- \(t = 4\)
Now plug the values into the formula:
\[ A = 800(1 + (0.15)(4)) \]
Calculating inside the parentheses first:
\[ 0.15 \times 4 = 0.6 \]
So now we have:
\[ A = 800(1 + 0.6) = 800(1.6) \]
Now multiply:
\[ A = 800 \times 1.6 = 1280 \]
The total amount after 4 years will be \(A = 1280\) dollars. To find out how much the student earned in interest, you subtract the principal from the total amount:
\[ \text{Interest earned} = A - P = 1280 - 800 = 480 \]
So, after 4 years, the student will have earned $480 in interest.