Suppose you are going to receive $9,500 per year for six years. The appropriate

Question

Suppose you are going to receive $9,500 per year for six years. The appropriate interest rate is
11 percent.
(a) What is the present value of the payments if they are in the form of an ordinary annuity?
(Hint: C = $9500) (1 Points)
(b) What is the present value if the payments are an annuity due? (1 Points)
(c) Suppose you plan to invest the payments for six years. What is the future value if the
payments are an ordinary annuity? (1 Points)
(d) Suppose you plan to invest the payments for six years. What is the future value if the
payments are an annuity due? (1 Points)
(e) Which has the higher present value, the ordinary annuity or annuity due? Which has the
higher future value? (1 Points)

Explanation / Answer

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

P - Periodic payment

r - rate per period

n - number of periods

PV of annuity = 9500*((1-(1+0.11)^(-6)) / 0.11) = $40190.11

b.

PV of annuity due = PV of ordinary annuity * (1+r)

PV of annuity due = 40190.11 * (1+0.11) = $44611.02

c.

FV of annuity = P*[((1+r)^n - 1)/r]
P - Periodic payment
r - rate per period
n - number of periods
FV of annuity = 9500*(((1+0.11)^6 - 1)/0.11) = $75172.17

d.

FV of annuity due = FV of ordinary annuity * (1+r) = 75172.17*(1+0.11) = $83441.10

e.

PV of annuity due, and FV of annuity due will be higher.

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