Question

raul lent his sister $173. she paid him back with 14% interest. during this time, he had charged $180 on his credit card, and owed an additional 11% interest on the loan. how much did raul make/lose during this time?

Explanation:

Step1: Calculate interest from sister's loan

First, find the interest Raul earned from lending to his sister. The principal \( P_1 = \$173 \) and the interest rate \( r_1 = 14\% = 0.14 \). The interest formula is \( I = P \times r \), so the interest from the sister is \( I_1 = 173 \times 0.14 \).
\( I_1 = 173 \times 0.14 = 24.22 \)

Step2: Calculate interest on credit card debt

Next, find the interest Raul owed on his credit card. The principal \( P_2 = \$180 \) and the interest rate \( r_2 = 11\% = 0.11 \). Using the same interest formula, the interest on the credit card is \( I_2 = 180 \times 0.11 \).
\( I_2 = 180 \times 0.11 = 19.8 \)

Step3: Calculate net gain/loss

To find how much Raul made or lost, subtract the interest owed from the interest earned: \( \text{Net} = I_1 - I_2 \).
\( \text{Net} = 24.22 - 19.8 = 4.42 \)

Answer:

Raul made \(\$4.42\) during this time.