To calculate the monthly payment for a car purchase, you can use the formula for calculating a loan payment. In this case, the car costs $10,000, the interest rate is 5.9%, and the loan term is 4 years.
1. Convert the annual interest rate to a monthly rate by dividing it by 12:
5.9% / 12 = 0.59% per month
2. Convert the loan term to months:
4 years * 12 months/year = 48 months
3. Use the following formula to calculate the monthly payment:
\[ \text{Monthly Payment} = \frac{P \cdot r \cdot (1+r)^n}{(1+r)^n - 1} \]
Where:
- P = Principal amount (loan amount) = $10,000
- r = Monthly interest rate = 0.59% or 0.0059
- n = Total number of payments = 48
4. Plug in the values into the formula:
\[ \text{Monthly Payment} = \frac{10,000 \cdot 0.0059 \cdot (1+0.0059)^48}{(1+0.0059)^48 - 1} \]
5. Calculate the monthly payment:
\[ \text{Monthly Payment} = \frac{10,000 \cdot 0.0059 \cdot (1.0059)^48}{(1.0059)^48 - 1} \]
\[ \text{Monthly Payment} = \frac{10,000 \cdot 0.0059 \cdot 1.33129}{1.33129 - 1} \]
\[ \text{Monthly Payment} = \frac{62.29}{0.33129} \]
\[ \text{Monthly Payment} \approx $188.12 \]
Therefore, the monthly payment for a $10,000 car at 5.9% interest for 4 years would be approximately $188.12.
