Question

Consolidated Decatur Bank is offering you a 30-year mortgage with an APR of 3.75%. What would be the monthly payment on this loan, per $1,000 borrowed? Suppose now they offer you the special deal of paying half of the monthly payment each two weeks (a total of 26 payments per year). With this modification, how long will it take to pay off the mortgage if the EFF of the loan is unchanged?

Answer 1

Monthly Payment Calculation:

Given, APR (Annual percentage rate)= 3.75%

Amount of Loan = $1000

A. Monthly payment = Principal X r(1+r)'n /(1+r)'n-1

Where Principal Amount =$ 1000

r= Interest rate = 3.75% = 0.0375/12 =0.003125

n = No. of Years of Payments = 30

by substituting the formula above, We get= $1000 X 0.003125(1+0.003125)'30 /(1+0.003125)'30 -1

= 3.431639/0.098125

=$34.97226

Case II:

Monthly payment = Principal X r(1+r)'n /(1+r)'n-1

Where Principal Amount =$ 1000

r= Interest rate = 3.75% = 0.0375/26 = 0.001442

n = No. of Years of Payments = 30

by substituting the formula above, We get= $1000 X 0.001442(1+0.001442)'30 /(1+0.001442)'30 -1

= 1.5060/0.044186

=$34.08372

There it will take 29.34 Years(i.e. $1000/$34.08372) to pay off the mortgage if EFF of loan is unchanged.