# Solving for the Interest Rate or Number of Years when Present and Future Lump sums are known

The basic steps in solving for the interest Rate or number of years when the present and future lump sums are known are as follows:

1. Enter the proper payments per year. You first must type in the appropriate number (e.g. monthly would be 12, quarterly would be 4, etc.), then push the cream colored key , then the P/YR key.
2. Now enter the present value. In this type of problem, the direction of the cash flow is important. Consequently, either the present value is received (and thus is positive) or it is paid (such as in an investment and is given a negative sign.) It is usually easier to develop a habit of treating the present value as and investment and giving it a negative sign. This is done by entering the appropriate amount, press the change sign key to indicate a cash outflow, then press the PV key.
3. Next enter the lump sum amount to be received in the future, then press the FV key.
4. If you are solving for the number of years, 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. If instead, you are solving for the interest rate, enter the number of years by pushing the appropriate number, then the cream colored key , then the xP/YR key.
5. Finally, if you are solving for the number of years, press the n key. The display will show the number of periods. Then press the RCL key, then the cream colored key , then the xP/YR key. The display then shows the number of years. If instead, you are solving for the interest rate, simply press the I/YR key.

Now let's try a problem of each type. First, consider that you buy a \$1000 US Savings Bond that matured in five years and pay \$680.58 for it. What is the interest rate the bond is paying?

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 cost of the bond is \$680.58. That indicates that the present value of the bond is \$680.58. 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, the cream colored key , 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 present value by pressing 680.58, then the change sign key to indicate a cash outflow, then press the PV key.
5. Next we enter the Future Value by pressing 1000 and then the FV key.
6. Finally, we press the I/YR key to compute the answer. The display then shows 8.00.

Now let's try another problem, this time solving for the number of years. Once again, consider that you buy a \$1000 US Savings Bond and pay \$680.58 for it. If the bond pays 8%, how many years will it take for the bond to reach maturity?

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 cost of the bond is \$680.58. That indicates that the present value of the bond is \$680.58. We know that the bond pays an 8% (I/YR) annual interest rate. 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, the cream colored key , then the P/YR key.
3. Next we will enter the interest rate by pressing 8 and the I/YR key.
4. Now we will enter the present value by pressing 680.58, then the change sign key to indicate a cash outflow, then press the PV key.
5. Next we enter the Future Value by pressing 1000 and then the FV key.
6. Finally, we press the press the n key. The display shows the 5, number of periods. Then press the RCL key, then the cream colored key , then the xP/YR key. The display again shows 5, this time reflecting the number of years. (In this case, the number of periods is equal to the number of years since the compounding period is once per year.)

Would you like to review the mathematics of this calculation?