Question

Consider a CPM loan in the amount of $150,000 with an interest rate of 4 percent with a 15 year maturity. What will be the monthly payment on the loan? If this loan had a maturity of 25 years, what would be the monthly payment?

Answer 1

Monthly Payment if the Maturity of the Loan is 15 Years

The Monthly payment is calculated by using the following formula

Monthly Payment = [P x {r (1 + r) ⁿ}] / (1 + r) ⁿ – 1

Loan Amount (P) = $150,000

Monthly Interest Rate (r) = 0.3333% [4% / 12 Months]

Number of Periods (n) = 180 Months [15 Years x 12 Months]

Monthly Payment = [P x {r (1 + r) ⁿ}] / (1 + r) ⁿ – 1

= [$150,000 x {0.003333 x (1 + 0.003333)¹⁸⁰}] / [(1 + 0.003333)¹⁸⁰ – 1]

= [$150,000 x {0.003333 x 1.82030}] / [1.82030 – 1]

= [$150,000 x 0.0060676] / 0.82030

= $1,109.53 per month

“Monthly Payment = $1,109.53 per month”

Monthly Payment if the Maturity of the Loan is 12 Years

The Monthly payment is calculated by using the following formula

Monthly Payment = [P x {r (1 + r) ⁿ}] / (1 + r) ⁿ – 1

Loan Amount (P) = $150,000

Monthly Interest Rate (r) = 0.3333% [4% / 12 Months]

Number of Periods (n) = 300 Months [25 Years x 12 Months]

Monthly Payment = [P x {r (1 + r) ⁿ}] / (1 + r) ⁿ – 1

= [$150,000 x {0.003333 x (1 + 0.003333)³⁰⁰}] / [(1 + 0.003333)³⁰⁰ – 1]

= [$150,000 x {0.003333 x 2.71376}] / [2.71376 – 1]

= [$150,000 x 0.0090458] / 1.71376

= $791.76 per month

“Monthly Payment = $791.76 per month”