Question

A lump sum payment of $1,000 is due at the end of 5 years. The nominal interest rate is 10%, semiannual compounding. Which of the following statements is/are INCORRECT? Why?

a.    The present value of the $1,000 would be greater if interest were compounded monthly rather than semiannually.

b.    The periodic rate is greater than 5%.

c.    The periodic interest rate is 5%.

d.    The present value would greater if the lump sum were discounted back for more periods.

e.    The PV of the $1,000 lump sum received at year 5 has a higher present value than the PV of a 5-year, $200 ordinary annuity.

Answer 1

a. Incorrect - Because as the number of compounding periods increase, Present value decreases.

PV = FV/(1+r)^n

b. Incorrect - Periodic rate is 5%.

Preiodic rate = Annual rate/No. of compounding periods = 10%/2 = 5%

c. Correct - Periodic rate is 5%.

d. Incorrect - Present value decreases with increase in number of compounding periods

e. Incorrect

PV of lumpsum = 1000/(1+0.1)^5 = $620.92

PV of annuity:

PV of annuity = P*[(1-(1+r)^(-n)) / r]

P - Periodic payment

r - rate per period

n - number of periods

PV of annuity = 200*((1-(1+0.1)^(-5)) / 0.1) = $758.16