- FINANCIAL CALCULATOR SOLUTION
Inputs: 3 5 0 100
Output: 315.25
Note that in annuity problems, the PMT key is used in conjunction with the N and I
keys, plus either the PV or the FV key, depending on whether you are trying to find
the PV or the FV of the annuity. In our example, you want the FV, so press the FV key
to get the answer, $315.25. Since there is no initial payment, we input PV 0.
- SPREADSHEET SOLUTION
72 CHAPTER 2 Time Value of Money
Most spreadsheets have a built-in function for finding the future value of an annuity.
In Excel,we could put the cursor on Cell E4, then click the function wizard, Financial,
FV, and OK to get the FV dialog box. Then, we would enter .05 or B1 for Rate, 3 or
E2 for Nper, and 100 for Pmt. (Like the financial calculator approach, the payment
is entered as a negative number to show that it is a cash outflow.) We would leave Pv
blank because there is no initial payment, and we would leave Type blank to signify
that payments come at the end of the periods. Then, when we clicked OK, we would
get the FV of the annuity, $315.25. Note that it isn’t necessary to show the time line,
since the FV function doesn’t require you to input a range of cash flows. Still, the time
line is useful to help visualize the problem.
Annuities Due
Had the three $100 payments in the previous example been made at the beginningof
each year, the annuity would have been an annuity due.On the time line, each payment
would be shifted to the left one year, so each payment would be compounded for one
extra year.
Time Line:
05%1 2 3
100 100 100
105
110.25
115.76
FVA 3 (Annuity due) 331.01
ABCDE
1 Interest rate 0.05
2 Time 012 3
3 Cash flow 100 100 100
4 Future value 315.25
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70 Time Value of Money
