Shawn borrowed $132,600 at 4.25 percent for 30 years to purchase a home. Payments are to be paid monthly. If all payments are paid as agreed, how much total interest will be paid

Interest payment= $ 102,176.54  

Explanation:

When a loan is to be paid over a period of time using a series of periodic equal installments, it is called loan amortization. Each equal installment is meant to liquidate the principal and the accrued interest.

Total Interest payment = total payment over the loan life - Principal amount

The monthly equal installment is calculated as follows:

Monthly equal installment-= Loan amount/Monthly annuity factor

Monthly annuity factor  

=( 1-(1+r)^(-n))/r

Monthly interest rate (r)

= 4.25%/12= 0.354 %

Number of months ( n) in 30 years

= 12* 30 = 360

Annuity factor  

= ( 1- (1.00354)^(-360)/0.00354= 203.3252575

Monthly installment = 132,600/47.03  = $652.157

Total Interest payment = total payment over the loan life - Principal amount

                  = (652.157 × 360) -  132,600=  102,176.54  

Interest payment= $ 102,176.54  

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