Which of the following statements is correct?
A)A 15-year mortgage will have larger monthly payments than a 30-year mortgage.
B)If an account earns 3 percent per year compounded annually, then it also has an effective annual rate (EAR) of 3 percent.
C)The present value of a $500 perpetuity is greater if the interest rate is higher.
D)Statements a, b, and c are correct.
E)Only statements a and b are correct.

Question

Quizplus · Accepted Answer

Statement A is correct because a 15-year mortgage has a shorter repayment period, so the payments need to be larger to pay off the loan in a shorter time frame compared to a longer-term 30-year mortgage.

Statement B is correct because the effective annual rate (EAR) considers compounding, so if an account earns 3 percent compounded annually, its EAR is also 3 percent.

Statement C is incorrect because the present value of a perpetuity is independent of the interest rate. The formula for the present value of a perpetuity is PV = C/r, where C is the periodic payment and r is the discount rate. The PV does not change with changes in the discount rate (interest rate) since the payment is constant.

Therefore, only statements A and B are correct.

Which of the Following Statements Is Correct