Final answer:
The monthly payment for a $12,000 loan with a 6-year term and an annual interest rate of 3.7% is calculated using the loan amortization formula, which results in a payment of approximately $202.15 per month.
Step-by-step explanation:
To calculate the monthly payment for a $12,000 loan over 6 years with an annual interest rate of 3.7%, we can use the formula for an amortizing loan which is derived from the annuity formula:
Monthly Payment (M) = P * (i / (1 - (1 + i)^(-n)))
Where:
- P = principal amount ($12,000)
- i = monthly interest rate ( annual interest rate / 12 )
- n = total number of payments (6 years * 12 months per year)
First, convert the annual interest rate to a monthly interest rate:
i = 3.7% / 12 months = 0.0030833 (decimal form)
Next, calculate the total number of payments:
n = 6 years * 12 months/year
= 72 payments
Substitute the values into the formula and solve for M:
M = $12,000 * (0.0030833 / (1 - (1 + 0.0030833)^(-72)))
M = $12,000 * (0.0030833 / (1 - (1.0030833)^(-72)))
M ≈ $12,000 * 0.01684610
M ≈ $202.15
Therefore, the monthly payment for the loan is approximately $202.15.