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

Question

Quizplus · Accepted Answer

Statement a is true because a 15-year mortgage has a shorter term than a 30-year mortgage, so the monthly payments will be larger.
Statement b is false because the effective annual rate (EAR) takes into account the compounding frequency, so the EAR will be higher than the stated annual rate. For instance, if the 3 percent interest is compounded quarterly, then the EAR will be 3.02 percent.
Statement c is false because the present value of a perpetuity is calculated by dividing the annual cash flow by the discount rate. If the interest rate is higher, the present value will actually decrease. Therefore, only statements a and b are correct.

Which of the Following Statements Is Correct