Answer:
Approximately $259.30.
Step-by-step explanation:
To find the monthly payment for a loan, we can use the formula for the monthly payment of an amortized loan:
M = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
M = Monthly payment
P = Principal loan amount
r = Monthly interest rate (annual interest rate divided by 12)
n = Total number of monthly payments (number of years multiplied by 12)
Given:
Principal loan amount (P) = $9,800.00
Annual interest rate = 13.8%
Number of years (n) = 4
First, we need to calculate the monthly interest rate (r). We divide the annual interest rate by 12 and convert it to a decimal:
r = (13.8% / 12) / 100 = 0.138 / 12 = 0.0115
Next, we calculate the total number of monthly payments (n):
n = 4 years * 12 months/year = 48 months
Now, we can substitute the values into the formula to calculate the monthly payment (M):
M = (9800 * 0.0115 * (1 + 0.0115)^48) / ((1 + 0.0115)^48 - 1)
Using a calculator, we find:
M ≈ $259.30 (rounded to the nearest cent)
Therefore, the monthly payment for a $9,800.00 loan at a 13.8% interest for 4 years is approximately $259.30.
