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

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

  1. Enter the Payments/Year
  2. Enter the rest of the information you know
  3. Solve for the unknown.

Solving for the Interest Rate

Let's try it with a problem
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 (PV) 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.")

Now let's compute the problem

  1. Enter the Payments/Year.
    You first must type in the appropriate number (eg. monthly would be 12, quarterly would be 4, etc.), then push the orange SHIFT key , then the P/YR key.

    In our problem, first we must enter the appropriate payments per year by pushing 1, then push the orange SHIFT key , then the P/YR key .
  2.  

  3. Enter the rest of the information you know.
    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, then the next step would be to enter in the proper number of years. You first type the appropriate number, then push the orange SHIFT key , then the xP/YR key.

      In our problem, next, we will enter the number of years by pushing 5, then the orange SHIFT key
      , then the xP/YR key.

       

    • 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.

      In our problem, 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.

       

    • Next, enter the lump sum amount to be received in the future, then press the FV key.

      In our problem, next, we enter the Future Value by pressing 1000 and then the FV key.
  4.  

  5. Solve for the unknown.
    Finally, press the I/YR key to compute the answer.

    Correct Answer
    The display then shows 8.00.

 

Solving for the Number of Years

Let's try it with a problem
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. 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 (PV) 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.")

Now let's compute the problem

  1. Enter the Payments/Year.
    You first must type in the appropriate number (eg. monthly would be 12, quarterly would be 4, etc.), then push the orange SHIFT key , then the P/YR key.

    In our problem, first we must enter the appropriate payments per year by pushing 1, then push the orange SHIFT key , then the P/YR key .
  2.  

  3. Enter the rest of the information you know.
    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, then the next step would be to 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.

      In our problem, we will enter the interest rate by pressing 8 and the I/YR key.

       

    • 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.

      In our problem, 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.

       

    • Next, enter the lump sum amount to be received in the future, then press the FV key.

      In our problem, we enter the Future Value by pressing 1000 and then the FV key.
  4.  

  5. Solve for the unknown.
    Finally, press the N key. The display will show the number of periods. Then press the RCL key, then the orange SHIFT key , then the xP/YR key. The display then shows the number of years.

    In our problem, we press the press the N key. The display shows the 5, the number of periods. Then press the RCL key, then the orange SHIFT 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.)

    Correct Answer
    The correct answer is 5.


Would you like to review the mathematics of this calculation?


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