 
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:
 Enter the Payments/Year
 Enter the rest of the information you know
 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
 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
.
 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.
 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
 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
.
 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.
 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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Copyright © 2005 Dr. Jerry D. Belloit
