Bud is offering a house for sale for $180,000 with an assumable loan which was made 5 years ago for $140,000 at 8.75% over 30 years.Kelsey is interested in buying the property and can make a $20,000 down payment.A second mortgage can be obtained for the balance at 12.5% for 25 years.What is the effective cost of the combined loans,if Kelsey would like to compare this financing alternative to obtaining a first mortgage for the full amount?
A)10.63%
B)9.39%
C)9.04%
D)11.27%

Question

Quizplus · Accepted Answer

First, let's calculate the remaining balance on the first loan after 5 years of payments:
PV = $140,000
n = 25*12 = 300 months
i = 8.75%/12 = 0.007292
Using the formula: Remaining balance = PV * (((1+i)^n)-((1+i)^p))/((1+i)^n-1), where p is the number of payments made:
Remaining balance = $132,573.19

Now let's calculate the second mortgage amount:
Second mortgage amount = $180,000 - $20,000 - $132,573.19 = $27,426.81

Using the same formula as before, but with different values:
PV = $27,426.81
n = 25*12 = 300 months
i = 12.5%/12 = 0.010417
Second mortgage payment = $290.93

To calculate the effective cost, we need to find the total payments over the life of both loans and then find the interest rate that would make those payments equivalent to getting one loan for the full amount ($180,000).
Total payments with two loans:
First mortgage: $961.71/month * 300 months = $288,513
Second mortgage: $290.93/month * 300 months = $87,279
Total payments = $375,792
Now let's solve for the interest rate using the following formula:
PV = $180,000
n = 25*12 = 300 months
PMT = -$1,252.64 (the monthly payment for one loan of $180,000 at the unknown interest rate)
Using a financial calculator or Excel, we find that the interest rate that solves for PV = $180,000 is 9.39%.

Therefore, the effective cost of the combined loans is 9.39%, which is lower than the second mortgage rate of 12.5% but higher than the first mortgage rate of 8.75%. Kelsey should choose the combined loans option.

Bud Is Offering a House for Sale for $180,000 with an Assumable