Final answer:
The monthly payment on a $100,000 loan with a 10% annual interest rate for 15 years would be approximately $965.61. The loan balance at the end of nine years (108 months) would be approximately $68,899.08. The effective borrowing cost on the loan, considering a 3% origination fee and going to maturity, would be approximately 19.62%.
Step-by-step explanation:
To calculate the monthly payment on a loan, we can use the formula:
Monthly Payment = P * r * (1+r)^n / ((1+r)^n - 1)
where:
- P is the loan amount ($100,000)
- r is the monthly interest rate (10% / 12 = 0.00833)
- n is the number of monthly payments (15 years * 12 months = 180)
Plugging in the values:
Monthly Payment = $100,000 * 0.00833 * (1+0.00833)^180 / ((1+0.00833)^180 - 1)
Monthly Payment ≈ $965.61
After nine years (108 months), the loan balance can be calculated using the formula:
Loan Balance = P * (1+r)^n - (Monthly Payment * ((1+r)^n - 1) / r)
Plugging in the values:
Loan Balance = $100,000 * (1+0.00833)^108 - ($965.61 * ((1+0.00833)^108 - 1) / 0.00833)
Loan Balance ≈ $68,899.08
The effective borrowing cost takes into account any upfront fees or charges. If the lender charges 3 points at origination, which is 3% of the loan amount, the effective borrowing cost can be calculated by adding the points to the total interest paid and then dividing it by the loan amount:
Effective Borrowing Cost = (Total Interest Paid + Points) / Loan Amount
Plugging in the values:
Effective Borrowing Cost = ($965.61 * 180 + 0.03 * $100,000) / $100,000
Effective Borrowing Cost ≈ 19.62%
If the loan is prepaid at the end of year 9, the effective borrowing cost can be calculated by adding the points to the total interest paid and then dividing it by the remaining loan balance:
Effective Borrowing Cost = (Total Interest Paid + Points) / Remaining Loan Balance
Plugging in the values:
Effective Borrowing Cost = ($965.61 * 108 + 0.03 * $100,000) / $68,899.08
Effective Borrowing Cost ≈ 20.45%