Fundamentals of Financial Management (Concise 6th Edition)

Chapter 5 Time Value of Money 139

5-10 FINDING ANNUIT Y PAYMENTS, PERIODS,

AND INTEREST RATES

We can! nd payments, periods, and interest rates for annuities. Here! ve variables
come into play: N, I, PMT, FV, and PV. If we know any four, we can! nd the! fth.

5-10a Finding Annuity Payments, PMT

Suppose we need to accumulate $10,000 and have it available 5 years from now.
Suppose further that we can earn a return of 6% on our savings, which are cur-
rently zero. Thus, we know that FV! 10,000, PV! 0, N! 5, and I/YR! 6. We can
enter these values in a! nancial calculator and press the PMT key to! nd how large
our deposits must be. The answer will, of course, depend on whether we make
deposits at the end of each year (ordinary annuity) or at the beginning (annuity
due). Here are the results for each type of annuity:

N I/YR PV PMT FV

0 10000 End Mode

(Ordinary

Annuity)

5 6

–1,773.96

N I/YR PV PMT FV

0 10000 Begin Mode

(Annuity

Due)

5 6

–1,673.55

Thus, you must save $1,773.96 per year if you make payments at the end of each year,
but only $1,673.55 if the payments begin immediately. Note that the required payment
for the annuity due is the ordinary annuity payment divided by (1 # I): $1,773.96/1.06
! $1,673.55. Spreadsheets can also be used to! nd annuity payments.

5-10b Finding the Number of Periods, N

Suppose you decide to make end-of-year deposits, but you can save only $1,200
per year. Again assuming that you would earn 6%, how long would it take to reach
your $10,000 goal? Here is the calculator setup:

SEL

F^ TEST Compared to an ordinary annuity, why does an annuity due have a higher

present value?

If you know the present value of an ordinary annuity, how can you! nd the

PV of the corresponding annuity due?

What is the PVA of an ordinary annuity with 10 payments of $100 if the

appropriate interest rate is 10%? What would the PVA be if the interest rate

was 4%? What if the interest rate was 0%? How would the PVA values di# er

if we were dealing with annuities due? ($614.46; $811.09; $1,000.00;

$675.90; $843.53; $1,000.00)

Assume that you are o# ered an annuity that pays $100 at the end of each year

for 10 years. You could earn 8% on your money in other investments with equal

risk. What is the most you should pay for the annuity? If the payments began

immediately, how much would the annuity be worth? ($671.01; $724.69)