Question

Problem #2 (30%) To buy a house you ask a bank for a mortgage loan of $ 400,000, repayable a mortgage loan of $ 400,000, repayable in 30 years of monthly payments at a yearly interest rate of 3%. After 20 years (240 m yearly interest rate of 3%. After 20 years (240 monthly payments) you decide to pay of the remainder of the loan. A) What is your monthly payment? B) What sum you must pay to the bank to extinguish your loan?

Answer 1

(a)

Compute the monthly rate of interest, using the equation as shown below:

Monthly rate = Annual rate/ 12 months

                      = 3%/ 12 months

                      = 0.25%

Hence, the monthly rate of interest is 0.25%.

Compute the PVIFA at 0.25% and 360 months, using the equation as shown below:

PVIFA = {1 – (1 + Rate)^{-Number of periods}}/ Rate

                   = {1 – (1 + 0.0025)^-360}/ 0.25%.

             = 237.189381504

Hence, the PVIFA at 0.25% and 360 months is 237.189381504.

Compute the monthly payment of the loan, using the equation as shown below:

Monthly payment = Loan amount/ PVIFA_{0.25%, 360 months}

                               = $400,000/ 237.189381504

                               = $1,686.41613491

Hence, the monthly payment amount is $1,686.41613491.

(b)

Compute the PVIFA at 0.25% and 240 months, using the equation as shown below:

PVIFA = {1 – (1 + Rate)^{-Number of periods}}/ Rate

                   = {1 – (1 + 0.0025)^-240}/ 0.25%.

             = 180.310914412

Hence, the PVIFA at 0.25% and 240 months is 180.310914412.

Compute the PVIF at 0.25% and 240 months, using the equation as shown below:

PVIF = 1/ (1 + Rate)^{Number of periods}

              = 1/ (1 + 0.0025)²⁴⁰

         = 1/ 1.820754995

         = 0.54922271397

Hence, the PVIF at 0.25% and 240 months is 0.54922271397.

Compute the amount required to extinguish the loan, using the equation as shown below:

Required amount = {Loan amount – (Monthly payment*PVIFA_{0.25%, 240})}/ PVIF_{0.25%, 240}

                             = {$400,000 – ($1,686.41613491*180.310914412)}/ 0.54922271397

                             = {$400,000 - $304,079.235364}/ 0.54922271397

                             = $174,648.211365

Hence, the amount required to extinguish the loan is $174,648.211365.