Question

You are planning to buy a house in New Jersey. You put a 20% down payment, and 15-year mortgage rates are at 4.2% -Price of the house is $400,000.

a. Calculate the monthly payments.

b- Calculate the 1st month interest payment.

c-Calculate the 1st month principal payments

Answer 1

Given in the Question :
Price of the House = $400,000
Down Payment = 20%
Years of mortgage = 15 years
Mortgage Rates = 4.2%

Solution:
Down payment = 20% * 4,00,000
= $80,000

Remaining loan to be repaid (P) = $400,000 - $80,000
= $3,20,000

Number of monthly installments (n) = 15*12
= 180

Monthly rate of interest (r) = 4.2/100*12
= 0.35% or 0.0035 (This is calculated for a month because the rate of interest given is per annum and we want to calculated installment for a month)

Equal Monthly Installments (EMI) = Principal Amount * Rate of Interest * (1+r)ⁿ / ((1+r)ⁿ - 1

= P * r * (1+r)ⁿ ÷ {(1+r)ⁿ -1}

= $3,20,000 * 0.35% * (1 + 0.35%)¹⁸⁰ ÷  {(1 + 0.35%)¹⁸⁰ -1}

= $3,20,000 *0.0035 * (1+0.0035)¹⁸⁰ ÷ {(1 + 0.0035)¹⁸⁰ -1}     

= $3,20,000 * 0.0035* (1.0035)¹⁸⁰ ÷ {(1.0035)¹⁸⁰ -1}     

= $3,20,000 * 0.0035 * (1.8755) ÷   {(1.8755) -1 }

= $2100.612 ÷ {0.8755}

= $2,399.201


A) Therefore, the Equal Monthly Installments will be equal to $2,399

B) The first month interest payment will be = Outstanding Principal amount * rate of interest

= P * r

= $320000 * 0.35%

= $320000 * 0.0035

= $1,120

C. First month's principal payment = Monthly Installment Amount - First Month's interest payment (As EMI is the sum of interest on the pending principal and the principal paid in that installment)

= $2,399 - 1,120

= $1,279