Question

# You are borrowing \$245,000 to purchase a home. The loan agreement requires a monthly payment based...

You are borrowing \$245,000 to purchase a home. The loan agreement requires a monthly payment based upon a 4.5% quoted APR over 20 years. What is your monthly mortgage payment?

Given the following information,

Loan amount = P = 245,000

Term in years = 20

Total number of monthly payments (mt) = 20*12 = 240

Annual Percentage Rate = APR = 4.5% = 0.045

Monthly interest rate (r/m) = 0.045/ 12 = 0.00375

Calculation of monthly payments, using the following formula,

Monthly Payments = (P*(r/m))/ (1-(1+(r/m))^(-mt)))

Substituting the above given values, we get

Monthly Payments = (245000*(0.00375))/ (1-(1+(0.00375))^(-240)))

Monthly Payments = (245000*(0.00375))/ (1-(1.00375)^(-240))

Monthly Payments = 918.75/ (1-(1.00375)^(-240))

Monthly Payments = 918.75/ (1-0.4073)

Monthly Payments = 918.75/ 0.5927

Monthly Payments = 1549.99

Therefore, the monthly mortgage payment is \$1549.99

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