Given a loan amount P an annual interest rate r and the leng

Given a loan amount P, an annual interest rate r, and the length of the loan in years, find the monthly payment R necessary to pay off the loan by completing parts a through c. Represent the number of monthly payments by n. amount, $140,000; rate, 6%; time, 20 years

Solution

Rate = 0.06 / 12 = 0.005 or 0.5% ( since it is monthly compunding)

Number of periods = 20 * 12 = 240

Present value = Annuity * [ 1 - 1 / ( 1 + R)ⁿ] / R

140,000 = Annuity * [ 1 - 1 / ( 1 + 0.005)²⁴⁰] / 0.005

140,000 = Annuity * 139.581

Annuity = $1,003

Monthly payment is $1,003.