On June 1, you borrowed $195,000 to buy a house. The mortgage rate is 5.25 percent. The loan is to be repaid in equal monthly payments over 15 years. All taxes and insurance premiums are to be paid separately. The first payment is due on July 1. How much of the first payment applies to the principal balance

Amount of the payment to be applied to the principal is $714.43

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.

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)

= 5.25/12 = 0.4375%,

Number of months

= 15 * 12 = 180

Annuity factor

= (1 - (1.004375) ^ (15*12) 0/0.004375

=124.39

Monthly installment

= 195,000/124.39

=1567.561

Interest due in first month

= 0.4375% * 195,000

= 853.125

Amount of the payment to be applied to the principal

= 1,567.561 - 853.125

=$714.43