Calculating the Present Value of a Future Lump Sum

The basic steps in calculating the present value of a future lump sum are as follows:

1. Enter the proper payments per year. You first must type in the appropriate number (eg. monthly would be 12, quarterly would be 4, etc.), then push the cream colored key , then the P/YR key.
2. The order of the next three steps is not important, but I recommend that you follow across the financial tour of your calculator from left to right. If you do this, then the next step would be to enter in the proper number of years. You first type the appropriate number, then push the cream colored key , then the xP/YR key.
3. Now enter the appropriate interest rate per year. This is done by entering the appropriate annual interest rate as a whole number, not as a decimal (the calculator will convert it to decimal automatically), then pressing the I/YR key.
4. Next enter the lump sum amount to be received in the future, then press the FV key.
5. Finally all that is necessary is push the PV key.

Now let's try a problem. Consider that you buy a \$1000 US Savings Bond that will mature in five years and paid 8% interest per year. How much should you pay today for the bond?

First let's see what we know. We know that the bond will be worth \$1000 in five years. That indicates that the future value (FV) of that bond is \$1000. We know that the number of years (xP/YR) is 5. We know that the annual interest rate is 8% (8 is the I/YR). Finally, we may assume that the periods per year is one since we are not told it is monthly, quarterly, etc. (If the payments per year would have been, for example, monthly, the problem would have read, ". . . paid 8% per year, compounded monthly.")

1. Now let's compute the problem.
2. First we must enter the appropriate payments per year by pushing 1, then the P/YR key.
3. Next we will enter the number of years by pushing 5, then the cream colored key , then the xP/YR key.
4. Now we will enter the interest rate per year by pushing 8 and then pressing the I/YR key.
5. Next we enter the Future Value by pressing 1000 and then the FV key.
6. Finally, we press the the PV key to compute the answer. The display then shows -680.58 if the display was set to show two decimal places. Note that the answer is negative. This indicates that the direction of the cash flow is out. (This is logical if we will be getting \$1000 in the future, we must pay \$680.58 now.)

Would you like to review the mathematics of this calculation?