Question

Which of the following statements is most correct?

Select one:

a. Other things equal, a 15-year mortgage will have smaller monthly payments than a 30-year mortgage of the same amount and same interest rate.

b. An investment's periodic interest rate will always be equal to or greater than its nominal interest rate.

c. Other things equal, A 5-year $100 annuity due will have a smaller present value than a 5-year $100 ordinary annuity.

d. An investment's nominal interest rate will always be equal to or smaller than its effective annual rate.

e. If an investment pays 10 percent interest compounded annually, its effective rate will be greater than 10 percent.

d and e are wrong

Answer 1

Answer: [d] An investment's nominal interest rate will always be equal to or smaller than its effective annual rate.

The EAR is given by: (1+r/m)^m-1, where m = the number of times compounding is done within a year.

If m = 1 [for annual compounding], EAR will be equal to r, the nominal rate.

If m>1, EAR will be greater than r.

Hence, nominal interest rate will be equal or smaller than EAR.

Let nominal rate be 12% per annum.
With annual compounding EAR = (1+0.12/1)^1-1 =	12.00%
With half yearly compounding EAR = (1+0.12/2)^2-1 =	12.36%
With quarterly compounding EAR = (1+0.12/4)^4-1 =	12.55%
As can be seen from the above:
Nominal interest rate = EAR, when it is annual compounding, as in the 1st case.
When compounding is done more than once in a year [as in the last two cases]
Nominal interest rate < EAR.
Hence, nominal interest rate is equal to or smaller than EAR.