Find the present values of the following ordinary annuities: a. PV of $400 each six months for five years at a simple rate of 12 percent, compounded semiannually b. PV of $200 each three months for five years at a simple rate of 12 percent, compounded quarterly c. The annuities described in parts (a) and (b) have the same amount of money paid into them during the five-year period and both earn interest at the same simple rate, yet the present value of the annuity in part (b) is $31.46 greater than the one in part (a). Why does this occur?

Expert Answer Ravpar Ravpar answered this Was this answer helpful? 1 0 1,304 answers

a) Effective annualized rate = (1 + 12%/2)^2 - 1 = 12.36%

Use PV formula in excel or calculator

PV(rate = 12.36%/2, nper = 5*2, pmt = 400, fv = 0, 0) = $2,919.09

b) Effective annualized rate = (1 + 12%/4)^4 - 1 = 12.55%

PV(rate = 12.55%/4, nper = 5*4, pmt = 200, fv = 0, 0) = $2,937.96

c) The difference is due to the compounding effect. You could observe that the effective rate of return is higher in b than in a although their simple rates are different.

My question now is in bold below:

With the answer to a) being $2,919.09 and the answer to b) being $2,937.96; yet part c) states "...yet the present value of the annuity in part (b) is $31.46 greater than the one in part (a)." Using the answers given by Ravpar there is a difference of $18.87 not $31.46 as stated in the original question. Please respond to this.