 
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:
 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.
 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.
 Next enter the lump sum amount to be received in the future, then press
the FV key.
 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.
 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.")
 Now let's compute the problem.
 First we must enter the appropriate payments per year by pushing 1, the
cream colored key , then
the P/YR key.
 Next we will enter the number of years by pushing 5, then the cream
colored key , then the
xP/YR key.
 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 we enter the Future Value by pressing 1000 and then the FV
key.
 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.")
 Now let's compute the problem.
 First we must enter the appropriate payments per year by pushing 1, the
cream colored key , then
the P/YR key.
 Next we will enter the interest rate by pressing 8 and the I/YR
key.
 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 we enter the Future Value by pressing 1000 and then the FV
key.
 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?
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Copyright © 2006 Dr. Jerry D. Belloit
