Final answer:
The monthly loan payment for a $26,000 loan over 4 years at a 4.99% interest rate with monthly compounding is approximately $598.64, which is option B.
Step-by-step explanation:
To calculate the monthly loan payment for a $26,000 loan fully amortized over 4 years with a nominal interest rate of 4.99% and monthly compounding interest, we can use the formula for the monthly payment of an installment loan:
M = P [ i(1 + i)ⁿ ] / [ (1 + i)ⁿ – 1 ]
Where:
- M = Monthly payment
- P = Principal amount ($26,000)
- i = Monthly interest rate (annual rate/12)
- n = Total number of payments (loan term in months)
First, we convert the annual rate to a monthly rate:
i = 4.99% / 12 = 0.0041575
Next, we find the total number of payments for 4 years:
n = 4 years × 12 months/year = 48 months
We can now plug these values into the formula to calculate the monthly payment:
M = 26,000 [0.0041575(1 + 0.0041575)⁴⁸] / [(1 + 0.0041575)⁴⁸ – 1]
After calculating, the monthly payment (M) comes out to approximately $598.64, which means that option B is the correct answer.