Answer:
To calculate the amount of interest in the first payment, we need to determine the monthly interest rate and the remaining principal balance after the first payment.
First, let's calculate the monthly interest rate. The annual interest rate is given as 20%. To convert it to a monthly rate, we divide it by 12 (the number of months in a year):
\[
\text{Monthly Interest Rate} = \frac{20\%}{12} = 0.0167
\]
Next, we need to calculate the remaining principal balance after the first payment. The loan amount is $2,000, and the monthly payment is $75. Since the loan term is 3 years (36 months), the remaining principal balance after the first payment can be calculated as:
\[
\text{Remaining Principal Balance} = \text{Loan Amount} - \text{Monthly Payment}
\]
\[
\text{Remaining Principal Balance} = \$2,000 - \$75 = \$1,925
\]
Now, we can calculate the interest for the first payment. The interest is calculated based on the remaining principal balance:
\[
\text{Interest} = \text{Remaining Principal Balance} \times \text{Monthly Interest Rate}
\]
\[
\text{Interest} = \$1,925 \times 0.0167 \approx \$32.08
\]
Therefore, the amount of interest in the first payment is approximately $32.08.