To find the monthly payment for a [tex]$1,000 loan with an annual percentage rate (APR) of 2.5% over a one-year term, you can follow these steps:
1. Convert the annual interest rate to a monthly interest rate:
An APR of 2.5% annually is divided by 12 months to find the monthly interest rate.
\[
\text{Monthly Interest Rate} = \frac{\text{Annual Interest Rate}}{12} = \frac{2.5\%}{12} = \frac{0.025}{12} \approx 0.002083
\]
2. Define the loan parameters:
- Principal Amount (P): \$[/tex]1,000
- Number of Monthly Payments (n): 12 months
- Monthly Interest Rate (r): 0.002083
3. Use the formula for calculating the monthly payment on an installment loan:
[tex]\[
\text{Monthly Payment} = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1}
\][/tex]
4. Plug in the values:
[tex]\[
\text{Monthly Payment} = \frac{1000 \cdot 0.002083 \cdot (1 + 0.002083)^{12}}{(1 + 0.002083)^{12} - 1}
\][/tex]
5. Calculate the result:
When you perform the calculations, you will find that the monthly payment is approximately:
[tex]\[
\text{Monthly Payment} \approx 84.47
\][/tex]
Therefore, the monthly payment for a \[tex]$1,000 loan at an APR of 2.5% over a one-year term is approximately \$[/tex]84.47.
