Jade is considering taking out a 14-year loan with monthly payments of $195 at an APR of 2.9%, compounded monthly, and this equates to a loan of $26,898.98. Assuming that Jade's monthly payment and the length of the loan remain fixed, which of these is a correct statement

A. If the interest rate were 2.7%, the amount of the loan that Jade is considering would be more than $26,898.98

Explanation:

First the multiple option statements to complete the question ...

A. If the interest rate were 2.7%, the amount of the loan that Jade is considering would be more than $26,898.98.

B. If the interest rate were 2.5%, the amount of the loan that Jade is considering would be less than $26,898.98.

C. If the interest rate were 2.3%, the amount of the loan that Jade is considering would be less than $26,898.98.

D. If the interest rate were 3.1%, the amount of the loan that Jade is considering would be more than $26,898.98.

To answer the question, we look at an extreme scenario of 0% interest rate and see the minimum repayment Jade will make on the loan taken

Therefore,

Interest Rate = 0%

This means that the loan to be paid will be calculated as follows

Monthly payments x 12 Months x 14 Years

= $195 x 12 months x 14 years = $32, 760

The meaning of this outcome is that the lower the interest rate to be paid, the higher the size of the loan, because at 2.9% the loan = $26,898.98 and at 0% rate the loan = $32, 760.

The conclusion therefore is a 2.7% interest rate which is lower than 2.9% but not as low as the extreme 0% will cause the loan amount to be higher than $26,898.98. This affirms option A.

Options B and C are wrong because 2.5% and 2.3% are lower than 2.9%, therefore, the loan amount will be higher. Option D is also wrong because a 3.1% interest rate is higher than 2.9%, therefore, the amount should be lower not higher than $26,898.98