Question

A professional couple wishes to purchase a new home costing $750,000, make a 20 percent down payment, and finance the remaining $600,000. The rate quoted for a conventional 30-year loan is 6.5084 percent interest with 1.875 points and no other closing costs. If, immediately after the one hundred twentieth payment (10 years), the professional couple decides to sell the house, what will be the unpaid balance on the loan with the points added to it?

Answer 1

New home costing = $750,000

Down payment 20% = $750,000 * 0.2 = $150,000

Balance amount P = $750,000 - $150,000 = $600,000 is a finance amount

Loan, P = $600,000

Loan period n = 30 years

number of periods per year, q= 12

The number of periods n = 30*12 = 360

Rate of interest i = 6.5084% = 6.51% = 0.065

Points = 1.875 = $750,000 * 1.875/100 = $14062.50

Monthly payment for this loan is,

M = Pi/[q(1-[1+(i/q)]-nq)]

= 600000 * (0.065) /[12 (1 - [1+(0.065/12)]^-(30*12))

= 39000 / [12 (1 - [1 + 0.005)]^-(30*12))

= 39000 / [ 12 (1 - [0.05 ]^-(30*12))

= 39000 /[ 12 * (1 - 0.03)

= 39000 / 11.64

= $3350.52 per month

The couple has made payment till 10 years i.e. 120 monthly installments, so total payment made

= 3350.52 * 120 = $ 402, 062.64

Number of loan repayments remaining = 360 - 120 = 240

Outstanding loan amount = M * (1 - 1 / (1+i)ⁿ) / i

= 3350.52 * (1 - 1/(1+0.065)²⁴⁰) / 0.065

= 3350.52 * (1 - 1/ (