5. Joseph and three friends bought a $260,000 house close to the university at t

Question

5. Joseph and three friends bought a $260,000 house close to the university at the end of August last year. At that time, they put down a deposit of $10,000 and took out a mortgage for the balance. Their mortgage payments are due at the end of each month (September 30, last year was the date of the first payment) and are based on the assumption that Joseph and friends will take 20 years to pay off the debt. Annual nominal interest is 12 percent, compounded monthly. It is now February. Joseph and friends have made all their fall term payments and have just made the January 31 payment for this year. How much do they still owe?

Explanation / Answer

Monthly interest rate = 12% / 12 = 1%

Number of months = 12 x 20 = 240

Loan amount = $(260,000 - 10,000) = $250,000

Total cost of loan ($) = Loan amount x [(r x N) / {1 - (1 + r)-N}]

= 250,000 x [(0.01 x 240) / {1 - (1.01)- 240}] = 250,000 x [2.4 / {1 - 0.018}] = 250,000 x (2.4 / 0.9082)

= 660,647.43

Monthly payments ($) = Loan amount x [r x (1 + r)N] / [(1 + r)N - 1]

= 250,000 x [0.01 x (1.01)240] / [(1.01)240 - 1]

= 250,000 x [0.01 x 10.8926] / [10.8926 - 1]

= 250,000 x 0.1089 / 9.8926

= 2,752.70

Number of monthly payments from 30 Sept to 31 Jan are 5.

Amount of loan left after 5 monthly payments ($) = 660,647.43 - (5 x 2,752.70) = 660,647.43 - 13,763.5

= 646,883.93

Related Questions

Navigate

• Browse (All)
• Browse 5
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.