To calculate the monthly payment for a loan, you can use the formula for an amortizing loan:
M = P × (r(1 + r)n) / ((1 + r)n – 1)
Where:
- M = monthly payment
- P = principal loan amount (the initial amount borrowed)
- r = monthly interest rate (annual interest rate divided by 12)
- n = total number of payments (loan term in months)
In this case, we have:
- P = $30,000
- Annual interest rate = 12%, so monthly interest rate = 12% / 12 = 1% = 0.01
- Loan term = 5 years, so total number of payments = 5 * 12 = 60
Now, plug the values into the formula:
M = 30000 × (0.01(1 + 0.01)60) / ((1 + 0.01)60 – 1)
Calculating the above:
- (1 + 0.01)60 ≈ 1.8194
- M = 30000 × (0.01 * 1.8194) / (1.8194 – 1)
- M = 30000 × 0.018194 / 0.8194
- M ≈ 30000 × 0.022199
- M ≈ $665.97
Therefore, the monthly payment for a $30,000 loan at a 12% nominal interest rate over 5 years, compounded monthly, is approximately $665.97.