Question

Which of the following statements is NOT CORRECT, assuming positive interest rates?

A) A 5-year $100 annuity due will have a higher present value than similar ordinary annuity.

B) A 15-year, $100,000 mortgage will have larger monthly payments than an otherwise similar 30-year mortgage.

C) If an investment pays 10% interest compounded annually, its effective rate will also be 10%.

D) Securities A and B offer the same nominal rate of interest, but A pays interest quarterly and B pays semiannually. Investment B will have the higher present value.

E) An investment's nominal interest rate will always be equal to or greater than its effective annual rate.

The answer is E: I understand why E is the answer but I don't get why D is also not incorrect.

Answer 1

Answer.

This is because in case of quarterly interest payment, there will be opportunity of reinvesting that interest for another quarter. which increase the effective rate of interest in case of quarterly payment as compared to semiannually paid interest.

For example, Security A and B having face value $1000 has 8% annual interest rate

But Security A pays interest quarterly as $20

and security B pays interest $ 40 Semiannually.

Here in case of security A, there is opportunity to reinvest $20 for next 3 Months, which will make interest on security A equal to

=$20+$20*2%

=$20.40

This makes effective interest on security A more as compared to security B. Hence in NPV calculation higher rate of interest reduces the present value of security.

An increase in the discount rate decreases the present value. This is because a higher interest rate means you would have to set less aside today to earn a specified amount in the future.