A house is for sale for $250,000.You have a choice of two 20-year mortgage loans with monthly payments: (1)if you make a down payment of $25,000,you can obtain a loan with a 6% rate of interest or (2)if you make a down payment of $50,000,you can obtain a loan with a 5% rate of interest.What is the effective annual rate of interest on the additional $25,000 borrowed on the first loan?
A)1.00%
B)6.00%
C)12.95%
D)18.67%

Question

Quizplus · Accepted Answer

For option 1, with a down payment of $25,000, the loan amount will be $225,000. The monthly payment for the loan can be calculated using the formula:

P = (Pv*R) / (1 - (1 + R)^(-n))

where Pv is the present value of the loan amount ($225,000), R is the monthly interest rate (6%/12 = 0.5%), and n is the total number of payments over the life of the loan (20 years * 12 months = 240).

Using a financial calculator or spreadsheet, the monthly payment for this loan is $1,536.58.

For option 2, with a down payment of $50,000, the loan amount will be $200,000. Using the same formula as above with an interest rate of 5%/12 = 0.4167%, the monthly payment for this loan is $1,329.18.

The additional $25,000 borrowed on the first loan is the difference between the loan amounts for options 1 and 2, which is $225,000 - $200,000 = $25,000.

To find the effective annual rate of interest on this additional $25,000 borrowed, we can use the formula:

EAR = (1 + r/m)^m - 1

where r is the nominal interest rate (0.5%), and m is the number of times the interest is compounded in a year (12 for monthly payments).

Plugging in the values, we get:

EAR = (1 + 0.005/12)^12 - 1 = 0.1295 = 12.95%

Therefore, the best choice is option 2, which has a lower interest rate and a higher down payment. Borrowing the additional $25,000 on the first loan would result in an effective annual interest rate of 12.95%, which is much higher than the 5% rate offered by the second loan.

A House Is for Sale for $250,000