Question

Susan wants to buy a house for $200,000. US Bank will give her the loan at 3.5% for 30 years if she puts 20% down and Dacotah Bank will give her the loan at 3.8% for 30 years if she puts 10% down. There are NO other options. (15 PTS) a. Which loan should she sign up for? Pick one, no explanation needed. What is her monthly payment? (5 PTS) b. After 5 years, Susan is approached by a philanthropic group known as C.S.C. They offer to lend her $50,000 interest free for an indefinite period of time, provided she joins their group. Susan takes up the offer and uses the money to pay off some of her mortgage. What will be her new NPER (how many years will it take for her to pay off her remaining mortgage)? (5 PTS) c. After another 7 years, a private bank offers to take over the remaining mortgage at 3%. What will be her first month interest payment if she signs up with them? (To do this, find the remaining mortgage after 12 years. Use this mortgage amount as the new principle. First month interest payment will be the monthly rate multiplied by principle). (5 PTS) d. (Bonus Question): Assume, there is a $1,000 one-time processing fee for signing up with the private bank in the previous part (c). Does it make sense to move the mortgage over to the private bank @ 3%? Explain. (5 PTS).

Answer 1

Monthly Mortgage Payment formula = Loan * [ r * (1+r)^t] / [(1+r)^t - 1]; where r is the monthly applicable interest rate and t is tenure in months.

Option 1: 20% downpayment; Loan amount = $160000; interest rate = 3.5% p.a. or (3.5%/12) = 0.29% monthly and tenure = 360 months

Monthly Payment = 160000 * [0.29% * (1+0.29%)³⁶⁰] / [(1+0.29%)³⁶⁰ - 1] = 718.47

Option 2: 10% downpayment; Loan amount = $180000; interest rate = 3.8% p.a. or (3.8%/12) = 0.32% monthly and tenure = 360 months

Monthly Payment = 180000 * [0.32% * (1+0.32%)³⁶⁰] / [(1+0.32%)³⁶⁰ - 1] = 808.28

Susan shoud take option 1.

Assuming Susan chose option 1, her residual loan balance at the end of 5 years will be :

Loan balance after k months = Loan * [(1+r)^t - (1+r)^k] / [(1+r)^t - 1]

Loan balance after 60 months = 160000 * [(1+0.29%)³⁶⁰ - (1+0.29%)⁶⁰] / [(1+0.29%)³⁶⁰ - 1] = 143515.3

From this she pays $50000, and the balance left will be 93515.32. At the same monthly payment of 718.47, we can use excel to find out how many months to repay - we find that it will take another 164 months or 13 years and 8 months more.

Balance after 7 years = 51159.6 - this we derive by extrapolating in the excel sheet monthly repayment schedule. Now the first month interest will be = 51159.6 * 3% / 12 = 127.90