What monthly payment is required to amortize a loan of $35,000 over 10 yr if interest at the rate of 15%/year is charged on the unpaid balance and interest calculations are made at the end of each month? (Round your answer to the nearest cent.)
i = .15/12 = .0125
n = 10x12 = 120
35000 = pay(1 - 1.0125^-120)/.0125
35000 = pay(61.98284725
payment = $564.67
To calculate the monthly payment required to amortize a loan, we can use the formula for calculating the monthly payment on a loan with an amortizing schedule.
The formula for calculating the monthly payment on a loan is:
P = r * (1 + r)^n / ((1 + r)^n - 1)
Where:
P = Monthly payment
r = Monthly interest rate
n = Number of monthly payments
To find the monthly interest rate, we need to use the annual interest rate and convert it to a monthly rate.
In this case, the annual interest rate is 15%. To convert it to a monthly rate, we divide it by 12 (the number of months in a year), and then convert it to decimal form by dividing by 100.
Monthly interest rate = 15% / 12 / 100 = 0.0125
Next, we need to find the total number of monthly payments. Since the loan duration is 10 years, we multiply the number of years by 12 (the number of months in a year).
Number of monthly payments = 10 * 12 = 120
Now we can substitute these values into the formula to calculate the monthly payment:
P = 0.0125 * (1 + 0.0125)^120 / ((1 + 0.0125)^120 - 1)
Calculating this expression will give us the monthly payment required to amortize the loan of $35,000 over 10 years at an annual interest rate of 15% and with interest calculations made at the end of each month. Rounding the answer to the nearest cent will give the final result.