Academy of Financial Markets
Using your financial calculator
What is this document?
This brief tutorial will take you through the basic financial calculations covered in the AFM
course on Financial Market Mathematics. As it currently stands, this tutorial covers the HP10B,
HP10BII, HP12C, SHARP-EL738 and Sharp EL 733A calculators as these are the most
popular financial calculators on the market.
The current version of this document details the calculator techniques required to convert
Nominal Interest Rates into Annual Effective Rates as well as the basics of working with Present
and Future values and Internal Rates of Return.
PLEASE NOTE THAT THESE ARE ONLY GUIDELINES COMPILED BY AFM AND DO NOT
REPLACE THE NEED FOR THE STUDENT TO LEARN HOW TO USE THEIR OWN
CALCULATOR. PLEASE REFER TO THE USER MANUAL OF YOUR CALCULATOR TO
ENSURE THAT CALCULATIONS ARE DONE CORRECTLY AND FOR CALCULATIONS
WHICH ARE NOT COVERED BY THESE GUIDELINES!
Annual Effective Rate Calculations
The following formula converts a nominal rate (the rate that we are all used to seeing quoted for
different financial instruments) into an Annual Effective Rate. This is the effective rate that can
be used to compare differing financial instruments with differing compounding periods. It
enables us to compare different financial instruments easily in order to see which one offers the
maximum return.
The formula is as follows:
n
i

AER = 1 +  − 1
 n
Refer to section 3.5 of your textbook for more detail. Although one can input this formula
manually into a number of scientific calculators, financial calculators simplify this task a great
deal. The keystrokes for some financial calculators follow.
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Example 1:
What is the Annual Effective Rate of 10%, compounded monthly?
AER: Sharp EL 738
Key
Explanation
12
Compounding periods per year. This is monthly compounding, so we
make this 12.
Allowing further information to be given to the calculator. You thus tell
the calculator that you have 12 compounding periods, but the rate will
follow
This is the nominal rate. If we were quoted a nominal rate of 5%, we
would press 5.
This key allows us access to the EFF key we are going to press next.
This stands for "convert to EFFective rate".
, (x,y)
10
2ndF
EFF
Answer 1:
10.4713
AER: Sharp EL 733A
Key
Explanation
2ndF
This key gives access to the “Mode” key we are going to press next
Mode
Press repeatedly until “FIN” appears. This is to place the calculator in
the financial mode
Compounding periods per year. This monthly compounding, so make
this 12
This key gives access to the “EFF” key we are going to press next
This stands for “convert to EFFective rate”.
This is the nominal rate. If we were quoted a nominal rate of 5%, we
would type in 5.
Press this to get the answer
12
2ndF
EFF
10
=
Answer 1:
10.4713
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Example 2:
What is the Annual Effective Rate of 9%, compounded quarterly?
AER: Sharp EL 738
Key
4
, (x,y)
Explanation
Compounding periods per year. This is quarterly compounding, so we make
this 4.
Allowing further information to be given to the calculator. You thus tell the
calculator that you have 4 compounding periods, but the rate will follow
This is the nominal rate.
This key allows us access to the EFF key we are going to press next.
This stands for "convert to EFFective rate".
9
2ndF
EFF
Answer 2:
9.3083%
(To convert back to nominal annual rate: 4; , (x,y); 9.3083; 2ndF APR)
Note: to change the number of decimals displayed you need to follow these instructions:
Key
SET UP
0
0
3
Explanation
This brings you to the Set-up menu which contains various changeable
aspects of the calculator. Note that you need to select from the menu. You
should see DSP displayed first with a blinking “0”.
This is similar to you phoning a company and the electronic menu option
asks you to enter the appropriate number on the keypad.
This would select the menu number “0” which is for DSP (display). If you
want to see more options use your arrow keys.
After selecting the above “0”, it will take you to the display menu. The
number of decimals is set by the TAB function, thus select this option by
pressing “0”.
You will see “DIG(0-9)?” displayed on your screen. You need to enter the
number of decimal places the calculator will display when you do
calculations. It is recommended that you use 3 to be accurate.
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AER: HP 12C
Example 1:
What is the Annual Effective Rate of 10%, compounded monthly?
Key
g then end
f then clear fin
10 then ENTER
Explanation
Set payments to end mode
100 then CHS
This clears the memory of all the financial registers
This is the nominal rate
Compounding periods. 12 periods (monthly) divided throughout the
year as interest
This is mandatory in order to turn the 10 into a percentage
ENTER
PV, FV then +
Enters the -100 value into the formula
This set of keystrokes will return the Annual Effective Rate
12, n ÷ then i
Answer 1:
10.4713
Example 2:
What is the Annual Effective Rate of 9%, compounded quarterly?
Key
g then end
f then clear
fin
9 then
ENTER
4, n ÷ then I
100 then CHS
ENTER
PV, FV then +
Explanation
Set payments to end mode
This clears the memory of all the financial registers
This is the nominal rate
Compounding periods. 4 periods (quarterly) divided throughout the
year as interest
This is mandatory in order to turn the 9 into a percentage
Enters the -100 value into the formula
This set of keystrokes will return the Annual Effective Rate
Answer 2:
9.3083%
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HP 10B / 10BII
Example 1:
What is the Annual Effective Rate of 10%, compounded monthly?
Key
12
Orangeshift
P/YR
10,
Orangeshift
then NOM%
Orangeshift
then EFF%
Explanation
The compounding periods per year (in this case monthly)
This gives us access to the P/YR button we are going to press next.
This puts the 12 into the P/YR register in the calculator’s memory
This puts the 10% into the nominal % register in the calculator’s
memory
The calculator works out the effective % based on the NOM% register
Answer 1:
10.4713
Example 2:
What is the Annual Effective Rate of 9%, compounded quarterly?
Key
4
Orangeshift
P/YR
9, Orangeshift then
NOM%
Orangeshift then EFF%
Explanation
The compounding periods per year (in this case quarterly)
This gives us access to the P/YR button we are going to
press next.
This puts the 4 into the P/YR register in the calculator’s
memory
This puts the 9% into the nominal % register in the
calculator’s memory
The calculator works out the effective % based on the
NOM% register
Answer 2:
9.3083%
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Present Value, Future Value and Payments
One can work out the present value, future value, payments per period and a number of other
very important variables by simply inputting the known variables into a financial calculator.
All financial calculators have one very important feature in common. That is, they all have the
following buttons:
N – Number of periods for the calculation
I/YR – Interest per year (nominal)
PV – Present value (of loan or investment)
PMT – Payment
FV – Future Value
The difference, however, is in the technique that one uses to enter the known values into
these buttons on the calculator. The following examples will display how such techniques
differ from one calculator to the next.
Our examples here will supply the FV, PV PMT etc as given. However, the reader should keep
in mind that real world problems will require some degree of interpretation in order to obtain
such values.
Example 1:
PV = 1000
PMT = 0 (no additional capital investments except for re-investment of interest)
N = 1 year
Interest = 9% monthly compounding
FV = UNKNOWN
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TVM: Sharp EL 738
Key
2ndF
Explanation
This takes you to the Second Function Menu
P/Y
12
This selects how often you will pay / compound per year
12 Represents monthly payments in a full year.
This stands for “Enter” to link the valued “12” to the memory box
“P/Y”
You have to “exit” the memory box used, by pressing the clear button
ONCE! Now you are ready to capture the other data in the applicable
field.
12 stands for the number of periods the investment is held. This goes
into the N register
This puts 9% for the interest rate into the memory of the calculator
under ‘interest per year’
This puts 1000 into the memory of the calculator under Present Value
ENT
ON/C
12 then N
9 then I/Y
1000 then PV
0 then PMT
COMP then FV
This puts 0 into the memory of the calculator under Payment
Tells the calculator to COMPUTE the Future Value based on the
input variables
Answer 1:
1093.81
TVM: Sharp EL 733A
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The same example as above, but with quarterly compounding would result in the following
steps:
Sharp EL 738
Key
2ndF then P/Y
4 then ENT
ON/C
4 then N
9 then I/Y
1000 then PV
0 then PMT
COMP then FV
Explanation
This selects how often you will pay / compound per year
This puts 4 (quarterly) into the P/Y field indicating the frequency of
compounding per annum.
Exit the P/Y field
4 stands for the number of periods the investment is held. This goes
into the N register.
This puts 9% for the interest rate into the memory of the calculator
under ‘interest per year’
This puts 1000 into the memory of the calculator under Present Value
This puts 0 into the memory of the calculator under Payment
Tells the calculator to COMPUTE the Future Value based on the
input variables
Answer 1b:
1093.08
Note: The change between quarterly and monthly compounding may seem small, but with
a larger initial investment, this will make a substantial difference.
Example 2:
PV = 100 000
PMT = UNKNOWN
N = 3 years
Interest = 18% monthly compounding
FV = 0
Key
2ndF then P/Y
12 then ENT
ON/C
36 then N
18 then I/Y
100 000 then PV
0 then FV
COMP then PMT
Explanation
This selects how often you will pay / compound per year
This puts 12 (monthly) into the P/Y field indicating the frequency of
compounding per annum.
Exit the P/Y field
36 stands for the number of periods the debt is repaid over. This
goes into the N register.
This puts 18% for the interest rate into the memory of the calculator
under ‘interest per year’
This puts 100 000 into the memory of the calculator under Present
Value (current debt to be repaid).
This puts 0 into the memory of the calculator under Future Value
(representing that all the debt is repaid)
Tells the calculator to COMPUTE the monthly Payment based on
the input variables
Answer 2: 3615.24
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TVM: HP 12C
Example 1:
PV = 1000
PMT = 0
N = 1 year
Interest = 9% monthly compounding
FV = UNKNOWN
Key
F then clear fin
9, ENTER, 12 then
÷
Explanation
We first clear all the financial registers stored on this calculator
0 then PMT
12 then N
1000 then PV
Divide 9 by 12 to get monthly compounding
Press i to put the answer from above into the interest rate
memory
This puts 0 into the memory of the calculator under future value
12 months, because we are have a one year investment.
Puts 1000 into the PV memory register
FV
Computes the future value and puts it on the display
i
Answer 1:
1093.81
The same example as above, but with quarterly compounding would result in the following
steps:
Key
F then clear fin
9, ENTER, 12 then
÷
i
1000 then PV
0 then PMT
4 then N
FV
Explanation
We first clear all the financial registers stored on this calculator
We take the interest rate and divide it by 4 to get quarterly
compounding
This puts the answer for the interest rate into the memory of the
calculator under ‘i’
This puts 1000 into the memory of the calculator under Present
Value
This puts 0 into the memory of the calculator under Payment
4 stands for the number of quarters the investment is held. 4
quarters equals one year.
Computes the future value and puts it on the display
Answer 1b:
1093.08
Note: The change between quarterly and monthly compounding may seem small, but with
a larger initial investment, this will make a substantial difference.
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Example 2:
PV = 100 000
PMT = UNKNOWN
N = 3 years
Interest = 18% monthly compounding
FV = 0
Key
Explanation
F then clear fin
18, ENTER, 12 then
÷
We first clear all the financial registers stored on this calculator
We take the interest rate and divide it by 12 to get monthly
compounding
This puts the answer for the interest rate into the memory of the
calculator under ‘I’
This puts 100 000 into the memory of the calculator under Present
Value
36 months, because we are talking about three years here.
This puts 0 into the memory of the calculator under future value
This calculates the Payment amount and puts it on the calculator
display
i
100 0000 then PV
36 then N
FV then 0
PMT
Answer 2:
3615.24
TVM: HP 10B / 10BII
Example 1:
PV = 1000
PMT = 0
N = 1 year (12 periods)
Interest = 9% monthly compounding
FV = UNKNOWN
Key
12
Orangeshift then
P/YR
12 then N
9 then I/YR
1000 then PV
0 then PMT
FV
Answer 1: 1093.81
Explanation
The compounding periods per year (in this case monthly
compounding)
This sets the compounding periods to 12 per year
12 periods goes into the number of periods memory in the
calculator
This puts 9 into the memory of the calculator under Interest per
Year
This puts 1000 into the memory of the calculator under Present
Value
This puts 0 into the memory of the calculator under Payment
The Future Value is calculated based on the other variables
input
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The same example with quarterly compounding would result in the following steps:
Key
4
Orangeshift then
P/YR
12 then N
9 then I/YR
1000 then PV
0 then PMT
FV
Explanation
The compounding periods per year (in this case quarterly
compounding)
This sets the compounding periods to 4 per year
12 periods goes into the number of periods memory in the
calculator
This puts 9 into the memory of the calculator under Interest per
Year
This puts 1000 into the memory of the calculator under Present
Value
This puts 0 into the memory of the calculator under Payment
The Future Value is calculated based on the other variables
input
Answer 1b:
1093.08
Note: The change between quarterly and monthly compounding may seem small, but with a
larger initial investment, this will make a substantial difference.
Example 2:
PV = 100 000
PMT = UNKNOWN
N = 3 years (36 months)
Interest = 18% monthly compounding
FV = 0
Key
12
Orangeshift then
P/YR
36 then N
18 then I/YR
100 000 then PV
0 then FV
PMT
Explanation
The compounding periods per year (in this case quarterly
compounding)
This sets the compounding periods to 4 per year
36 periods goes into the number of periods memory in the
calculator (36 months)
This puts 18 into the memory of the calculator under Interest
per Year
This puts 100 000 into the memory of the calculator under
Present Value
This puts 0 into the memory of the calculator under Future
Value
The payment per period is calculated based on the other
inputs
Answer 2:
3615.24
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Internal Rate of Return (IRR) Calculations
The IRR procedure is designed to calculate the i (interest rate) of cash flows varying in
magnitude.
General note: All the below examples use annual cash flows (implying a P/YR = 1). For other
cash flow periods, the IRR answer must be multiplied by the corresponding P/YR to get the
correct annualised IRR (e.g. the calculated IRR from monthly cash flows must be multiplied by
12 to get an annualised IRR). However, the HP10BII calculator is the exception in this regard
(you have to specify the P/YR upfront), meaning your calculated IRR is automatically
annualised.
IRR: Sharp EL 738
Example 1:
Assume we have to invest R1 000 in order to buy some sort of equipment, and it is expected
that this equipment will give us the following cash flows in the years ahead.
Year 1 = R300
Year 2 = R400
Year 3 = R200
Year 4 = R600.
What is the IRR that we expect to earn given these cash flows.
Key
Explanation
CFI then 2ndF then
CA
This clears all the cash flow memory banks.
Now you are ready to capture the Cash Flow DATA
The first cash flow is negative R1000, so put it in and give it a
1000 then +/negative sign
ENT
Enters the R1000 into cash flow 0 (zero)
300 then ENT
Sets the first cash flow to 300 and moves to cash flow 2
400 then ENT
Sets the second cash flow to 400 and moves to cash flow 3
200 then ENT
Sets the third cash flow to 200 and moves to cash flow 4
600 then ENT
Sets the fourth cash flow to 600 and moves to cash flow 5
ON/C
This exits the cash flow capture mode.
2ndF then CASH then This sets all the values entered in the correct format (place in
2ndF then CA
time)
COMP
Tells calculator to compute the Internal Rate of Return
Answer 1:
16.71
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IRR: Sharp EL 733A
Key
1000 then +/CFj
300 then CFj
400 then CFj
200 then CFj
600 then CFj
Comp then IRR
Explanation
The first cash flow is negative R1000, so put it in and give it a
negative sign
Puts the R1000 into cash flow 0 (zero)
Sets the first cash flow to 300 and moves to cash flow 2
Sets the second cash flow to 400 and moves to cash flow 3
Sets the third cash flow to 200 and moves to cash flow 4
Sets the fourth cash flow to 600 and moves to cash flow 5
Tells calculator to compute the Internal Rate of Return
Answer 1: 16.71
IRR: HP 12C
Example 1:
Assume we have to invest R1 000 in order to buy some sort of equipment, and it is expected
that this equipment will give us the following cash flows in the months ahead. Year 1 = R300
Year 2 = R400 Year 3 = R200 Year 4 = R600.
What is the rate of return (Internal Rate of Return) that we earn on these cash flows.
Key
1000 then CHS
g then CF0
300, g then CFj
400, g then CFj
200, g then CFj
600, g then CFj
f then IRR
Explanation
The first cash flow is negative R1000, so put it in and give it a
negative sign
Puts the R1000 into cash flow 0 (zero)
Sets the first cash flow to 300 and moves to cash flow 2
Sets the second cash flow to 400 and moves to cash flow 3
Sets the third cash flow to 200 and moves to cash flow 4
Sets the fourth cash flow to 600 and moves to cash flow 5
Tells calculator to compute the Internal Rate of Return
Answer 1:
16.71
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IRR: HP 10B / 10BII
Example 1:
Assume we have to invest R1 000 in order to buy some sort of equipment, and it is expected
that this equipment will give us the following cash flows in the years ahead.
Year 1 = R300
Year 2 = R400
Year 3 = R200
Year 4 = R600.
What is the rate of return (Internal Rate of Return) that we earn on these cash flows.
Note; in this example, only one payment per year is received; so you need to set your
calculators to 1 payment per year. This can be done by pressing 1, OrangeShift then P/YR
Key
1000 then +/CFi
300 then CFj
400 then CFj
200 then CFj
600 then CFj
OrangeShift then IRR
Explanation
The first cash flow is negative R1000, so put it in and give it a
negative sign
Puts the R1000 into cash flow 0 (zero)
Sets the first cash flow to 300 and moves to cash flow 2
Sets the second cash flow to 400 and moves to cash flow 3
Sets the third cash flow to 200 and moves to cash flow 4
Sets the fourth cash flow to 600 and moves to cash flow 5
Tells calculator to compute the Internal Rate of Return
Answer 1:
16.71
NPV calculations
The NPV procedure is very similar to the IRR procedure, except for the:
• Allocation of zero (0) to cash flow zero
• Calculation/ computation of the “NPV” (which is actually the PV of the cash flows
concerned).
We hope that this guide has helped you to make sense of your financial
calculator.
Team
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