Firm has a $500,000 loan with 9% APR (compounded monthly)
Loan is 5-yr based on a 15-yr amortization, meaning loan payments will be calculated as if you take 15 years to pay off the loan, but actually must do so in 5 yr.
To do this, you make 59 equal payments based on the 15-yr amortization schedule and then make a final 60th payment to pay remaining balance.
1. What will the monthly payments be?
2. What will the final payment be?
To calculate the monthly payments and the final payment for the loan, we can use the formula for calculating the monthly payment on an amortized loan. This formula takes into account the loan amount, the annual interest rate, and the loan term. The formula is as follows:
Monthly Payment = (P * r) / (1 - (1 + r)^(-n))
Where:
- P is the principal amount (loan amount)
- r is the monthly interest rate (annual interest rate divided by 12 and expressed as a decimal)
- n is the total number of monthly payments (for a 5-year loan with monthly payments, n would be 60)
1. Monthly Payments:
In this case, the loan amount is $500,000 and the annual interest rate is 9%. To find the monthly interest rate, we divide the annual interest rate by 12 months: r = 9% / 12 = 0.75% or 0.0075 as a decimal. The total number of monthly payments is 60.
Using the formula, we can calculate the monthly payment:
Monthly Payment = (500,000 * 0.0075) / (1 - (1 + 0.0075)^(-60))
= $10,737.64
Therefore, the monthly payment will be approximately $10,737.64.
2. Final Payment:
To calculate the final payment, we need to determine the remaining balance after making the 59 equal payments based on the 15-year amortization schedule.
To find the remaining balance after 59 payments, we can calculate it using the amortization formula:
Remaining Balance = P * (1 + r)^n - (Monthly Payment * ((1 + r)^n - 1) / r)
Where:
- P is the principal amount (loan amount)
- r is the monthly interest rate
- n is the total number of monthly payments made
For the 59th payment, n will be 59. Using the amounts from the previous calculations, we can find the remaining balance after 59 payments:
Remaining Balance = 500,000 * (1 + 0.0075)^59 - (10,737.64 * ((1 + 0.0075)^59 - 1) / 0.0075)
= $39,101.29
Therefore, the final payment required to pay off the remaining balance will be $39,101.29.