interest rate of 2 percent per month or 12(2%) 24% per year, you would probably
want to buy the computer rather than lease it.
It is worth pointing out that the left side of the equation can not equal zero if you
put both the PV and PMT as positive numbers (assuming positive interest rates). If
you do this by mistake, most financial calculators will make a rude beeping noise,
while spreadsheets will display an error message.
In anExcelspreadsheet, you would use the same RATE function that we dis-
cussed earlier. In this example, enter 36 for Nper,78 for Pmt, 1988.13 for Pv, 0 for
Fv, and 0 for Type:RATE(36,78,1988.13,0,0).The result is again 0.02, or 2
percent.
Regarding how long you must save until you accumulate $1 million, you know
i 8%, PV 0 (since you don’t have any savings when you start), PMT 4,000
(it is negative since the payment comes out of your pocket), and FV 1,000,000 (it is
positive since you will get the $1 million). Substituting into Equation 2-6 gives:
(2-6a)
Using algebra, you could solve for n, but it is easier to find n with a financial calcula-
tor. Input I 8, PV 0, PMT 4000, FV 1000000, and solve for N, which is
equal to 39.56. Thus, it will take almost 40 years to accumulate $1 million if you earn 8
percent interest and only save $4,000 per year. On a spreadsheet, you could use the
same NPER function that we discussed earlier. In this case, enter 8% for Rate, 4000
for Pmt, 0 for Pv, 1000000 for Fv, and 0 for Type: NPER(8%,4000,0,1000000,0).
The result is again 39.56.
If you only plan to save for 20 years, how much must you save each year to accu-
mulate $1 million? In this case, we know that n 20, i 8%, PV 0, and FV
- The equation is:
(2-6a)
You could use algebra to solve for PMT, or you could use a financial calculator and in-
put N 20, I 8, PV 0, and FV 1000000. The result is PMT 21,852.21. On
a spreadsheet, you would use the PMT function, inputting 8% for Rate, 20 for Nper,
0 for Pv, 1000000 for Fv, and 0 for type: PMT(8%,20,0,1000000,0).The result is
again 21,852.21.
Write out the equation that is built into a financial calculator.
Explain why a financial calculator cannot find a solution if PV, PMT, and FV all are
positive.
Perpetuities
Most annuities call for payments to be made over some finite period of time—for
example, $100 per year for three years. However, some annuities go on indefinitely, or
perpetually, and these are called perpetuities.The present value of a perpetuity is
found by applying Equation 2-7.
(2-7)
Perpetuities can be illustrated by some British securities issued after the Napoleonic
Wars. In 1815, the British government sold a huge bond issue and used the proceeds
PV(Perpetuity)
Payment
Interest rate
PMT
i
.
(0)(10.08)^20 PMTa
(10.08)^20 1
0.08
b1,000,0000.
(0)(10.08)n(4,000)a
(10.08)n 1
0.08
b1,000,0000.
78 CHAPTER 2 Time Value of Money
76 Time Value of Money
