Question

You make a one-time deposit of $200 earned at your pizzeria job into a bank that pays simple interest. After 5 years, you check your balance and you have $230. How much did you earn in interest each year? Do not include a dollar sign in your answer. Round to the nearest cent (hundredth).(1 point)
$

Answer 1

To find out how much interest you earned each year, we can use the formula for simple interest:

\[ I = P \times r \times t \]

Where:
- \( I \) = total interest earned
- \( P \) = principal amount (initial deposit)
- \( r \) = annual interest rate (as a decimal)
- \( t \) = time in years

From the information given:
- Principal amount \( P = 200 \)
- Total balance after 5 years = $230
- Total interest earned \( I = 230 - 200 = 30 \)
- Time \( t = 5 \)

Now we can rearrange the simple interest formula to find the annual interest:

\[ r = \frac{I}{P \times t} \]

Substituting the values:

\[ r = \frac{30}{200 \times 5} \]
\[ r = \frac{30}{1000} \]
\[ r = 0.03 \]

Now we find the annual interest earned by multiplying the principal by the interest rate:

Annual interest earned = \( P \times r = 200 \times 0.03 = 6 \)

Thus, the amount earned in interest each year is:

\[ 6 \]

So the answer is:

6