Jim and Ann bought a house with a down payment of 9000 and a

Jim and Ann bought a house with a down payment of $9,000 and a $141,000 loan. The loan was for 25 years at a 4.8% interest rate. Closing costs amounted to an additional 1.4%. Two years later they were transferred and sold the house for what they paid for it, $150,000. The real estate agent charged a 4% fee for selling the house. Find the average monthly cost of the house taking into consideration the monthly payments, the costs of buying and selling, and the equity built up over 2 years. (Round your answer to the nearest cent.)

Solution

Purchase cost of house = $ 150000; Down payment = $9000; Loan amount = $141000; Interest rate = 4.8% p.a. or monthly rate of (4.8%/12) = 0.40%; tenure = 25 years or 300 months

Closing cost at time of purchase = 1.4% * 150000 = $2100

Monthly mortgage payment = Loan amount * [r * (1+r)^t]/[(1+r)^t - 1] ; where r is the applicable monthly rate and t is the tenure in months. Plugging in the values we get:

Monthly mortgage payment = 141000 * [0.40% * (1+0.40%)³⁰⁰] / [(1+0.40%)³⁰⁰ - 1] = 807.93

When the house is sold after 2 years, the residual loan balance will be :

Loan Amount * [(1+r)^t - (1+r)^k] / [(1+r)^t - 1] ; where k is the time period in months at which we require the residual balance and in this case k - 24 months. Plugging in the values we get:

141000 * [(1+0.40%)³⁰⁰ - (1+0.40%)²⁴] / [(1+0.40%)³⁰⁰ - 1] = 134,868.40

Hence the equity in the house has grown by (141000 - 134868.40) = 6131.6

The selling costs = 4% * 150000 = 6000

Now lets look at all the costs involved in buying and holding the house for 24 months:

Purchase Equity : 9000

Increase in equity at the time of sale = 6131.6 or monthly (6131.6/24) = 255.48

Purchase costs = 2100 or monthy (2100/24) = 87.5

Sale costs = 6000 or monthly (6000/24) = 250

Monthly mortgage payment = 807.93

Total monthly costs over 2 years = (87.5 +250 + 807.93) - 255.48 = 889.95