1. Financial calculators for Real Estate Finance
…or, everything you wanted to know about financial calculators, but were afraid to ask.

2. Overview Which calculator should you purchase?
Basic arithmetic calculations
Mortgages
Payments
Balances
Yields
DCF, NPV and IRR
Cash flows
NPV
IRR

3. Which calculator should you purchase?
For applications in real estate, finance and accounting, you want a financial calculator
Hewlett-Packard: 10bii, 10bii+, 12c, 17bii
The 10bii and 12c support only RPN entry, the 12c Platinum and 17bii allow for a choice between RPN and ALG entry, the 10bii+ supports only ALG
The 12c is the only HP calculator approved for CFA exams
Texas Instruments: BAII Plus
The BAII Plus supports only ALG entry
The BAII Plus is the only TI calculator approved for CFA exams

4. User manuals
User manuals for each of these are available online and are invaluable resources – they are full of additional examples similar to what is presented here and provide explanations of calculator functionality beyond what is covered in this tutorial:
HP 10bii:
HP 10bii+:
HP 12c:
HP 17bii:
TI BAII Plus:

5. Basic calculations RPN or ALG? RPN = Reverse Polish Notation
To find the solution to 1 + 2, enter “1” then “ENTER” then “2” then “+” – the correct answer, “3”, should be visible in the display.
The default (and, sometimes, only) mode for most HP calculators is RPN – RPN usually requires fewer keystrokes to arrive at a given solution and makes more efficient use of “stack” memory.
Hint: if there’s no key for “=” on your calculator, entry is based on RPN.
ALG = Algebraic notation
To find the solution to 1 + 2, enter “1” then “+” then “2” and then, finally, “=”, the correct answer, “3”, should be visible in the display.
The default mode for TI calculators is ALG.

6. Some Preliminaries for HP 10bII+
Make sure you “clear all” to erase any new information
Red arrow down key then the “C ALL” button gage
Make sure your payments per year is always set correctly!
1 for annual, 2 for semi-annual (bonds), 12 for monthly (mortgages)
Mortgage example: 12 then red arrow down key then the “P/YR” button
Next time you “clear all” the value for P/YR will display
Make sure the number of decimals you want to show is set correctly
Assume we want to display 4 decimals
Red arrow down key then the “DISP” button then the number of decimals you want to display (4 in this case)

7. Basic calculations
Mortgage calculations are based on the total number of compounding periods and the periodic interest rate. How are these determined using RPN notation?
Mortgage payments are made on a monthly basis for 30 years, how many compounding periods are there in a 30-year mortgage?
To find the total number of compounding periods, enter “30” then “ENTER” then “12” then “×”.
HP12b: Enter 360 for N
If the stated annual mortgage interest rate is 5%, what is the periodic interest rate?
The periodic interest rate is simply the annual rate divided by the number of compounding periods per year, enter “5” then “ENTER” then “12” then “÷”.
HP12b: Note that we enter 5 for I/YR

8. Mortgages – HP 10 bII+
Main keys used in calculations relating to mortgage loans:
N – total number of compounding periods
I/YR – annual (quoted) interest rate
PV – initial mortgage balance
PMT – periodic payment
FV – remaining mortgage balance at the end of a given number of compounding periods

9. Mortgages Conventions and helpful hints:
Enter information as if you are the lender – cash outflows, such as PV, should be entered as negative numbers, cash inflows, such as PMT, should be entered as positive numbers.
To change the sign of a number, use “CHS” or “+/-”
Outcomes are based on payments being made at the end of the month.
Information entered into any of the financial function keys remains as entered until either the register is cleared or the information is replaced.
To determine the payment associated with a change in the interest rate, just enter the new periodic rate into i and then press PMT to find the new payment – the values for n, PV and FV will remain unchanged
To clear the information stored in the financial function keys, enter “f” and then “x><y”

10. Mortgage payments – HP 10bII+
What is the monthly mortgage payment if you finance $225,000 of the purchase price of your new home with a fully amortizing 30-year fixed-rate, fixed-payment mortgage with a 5% annual interest rate?
Make sure that P/YR = 12
How much will you borrow from the lender?
PV = -225,000
How many payments?
N = 360
What is the balance remaining after making the last payment?
FV = 0
What is the monthly interest rate?
I/YR = 5.00
What is the monthly payment?
PMT = ? =

11. Mortgage payments – HP 10bII+
What is the monthly mortgage payment if you finance $225,000 of the purchase price of your new home with a fully amortizing 30-year fixed-rate, fixed-payment mortgage with a 5.5% annual interest rate?
Make sure that P/YR = 12
How much will you borrow from the lender?
PV = -225,000
How many payments?
N = 360
What is the balance remaining after making the last payment?
FV = 0
What is the monthly interest rate?
I/YR = 5.50
What is the monthly payment?
PMT = ? =

12. Mortgage payments
What is the monthly mortgage payment if you finance $335,000 of the purchase price of your new home with a fully amortizing 30-year fixed-rate, fixed-payment mortgage with a …
4.0% annual interest rate?
PMT = ? =
4.5% annual interest rate?
PMT = ? =
5.0% annual interest rate?
PMT = ? =
5.5% annual interest rate?
PMT = ? =
6.0% annual interest rate?
PMT = ? =

13. Mortgage payments – HP 10bII+
What is the monthly mortgage payment if you finance $225,000 of the purchase price of your new home with a fully amortizing 15-year fixed-rate, fixed-payment mortgage with a 5% annual interest rate?
How much will you borrow from the lender?
PV = -225,000
How many payments?
N = 180
What is the balance remaining after making the last payment?
FV = 0
What is the monthly interest rate?
I/YR = 5.00
What is the monthly payment?
PMT = ? =

14. Mortgage payments
What is the monthly mortgage payment if you finance $355,000 of the purchase price of your new home with a fully amortizing 15-year fixed-rate, fixed-payment mortgage with a …
4.0% annual interest rate?
PMT = ? =
5.0% annual interest rate?
PMT = ? =

15. Mortgage payments – HP 10bII+
What is the monthly mortgage payment if you finance $225,000 of the purchase price of your new home with a partially amortizing 30-year fixed-rate, fixed-payment mortgage with a $100,000 balloon payment due at maturity and a 5% annual interest rate?
How much will you borrow from the lender?
PV = -225,000
How many payments?
N = 360
What is the balance remaining after making the last payment?
FV = 100,000
What is the monthly interest rate?
I/YR = 5.00
What is the monthly payment?
PMT = ? =

16. Mortgage payments
What is the monthly mortgage payment if you finance $355,000 of the purchase price of your new home with a partially amortizing 30-year fixed-rate, fixed-payment mortgage with a $250,000 balloon payment due at maturity and a 5% annual interest rate?
PMT = ? =
What is the monthly mortgage payment if you finance $355,000 of the purchase price of your new home with a non-amortizing 30-year fixed-rate, fixed-payment mortgage with a $355,000 balloon payment due at maturity and a 5% annual interest rate?
A non-amortizing mortgage is frequently referred to as an interest-only loan as the payment in any month equals the monthly interest based on the initial loan balance.
PMT = ? =

17. Mortgage balances
What is the balance remaining monthly mortgage payment if, three years ago, you borrowed $225,000 of the purchase price of your new home with a fully amortizing 30-year fixed-rate, fixed-payment mortgage with a 5% annual interest rate?
What is the monthly payment?
PMT = ? =
What is the balance remaining after making 36 payments?
N = 36
FV = ? = 214,523.09

18. Mortgage balances
What is the balance remaining monthly mortgage payment if, five years ago, you borrowed $225,000 of the purchase price of your new home with a fully amortizing 30-year fixed-rate, fixed-payment mortgage with a 5% annual interest rate?
What is the monthly payment?
N = 360
I/YR = 5
PV = -225,000
FV = 0
PMT = ? =
What is the balance remaining after making 60 payments?
N = 60
FV = ? = 206,

19. Mortgage balances
If you borrowed $355,000 of the purchase price of your new home with a fully amortizing 30-year fixed-rate, fixed-payment mortgage with a 5% annual interest rate, what is the balance remaining after …
four years?
N = 360
I/YR = 5
PV = -355,000
FV = 0
PMT = ? = 1,
N = 48
FV = ? = 332,
ten years?
N = 120
FV = ? = 288,

20. Mortgage yield – HP 10bII+
If the monthly payment for the fully amortizing 30-year fixed-rate, fixed-payment mortgage used to finance $225,000 of the purchase price of your new home is $1500, what is the interest rate on your loan?
How much will you borrow from the lender?
PV = -225,000
How many payments?
N = 360
What is the balance remaining after making the last payment?
FV = 0
What is the monthly payment?
PMT = 1,500.00
What is the interest rate?
I/YR = ? =

21. Mortgage yield – HP 10bII+
If the monthly payment for the fully amortizing 30-year fixed-rate, fixed-payment mortgage used to finance $225,000 of the purchase price of your new home is $1250, what is the interest rate on your loan?
How much will you borrow from the lender?
PV = -225,000
How many payments?
N = 360
What is the balance remaining after making the last payment?
FV = 0
What is the monthly payment?
PMT = 1,250.00
What is the interest rate?
I/YR = ? =

22. Mortgage yield
If you borrowed $355,000 of the purchase price of your new home with a fully amortizing 30-year fixed-rate, fixed-payment mortgage, what is the annual interest rate associated with the loan if the monthly payment is …
$1,750?
i = .3556, y = 4.27%
HP 10bII+ I/YR = %
$2,500?
i = .6311, y = 7.57%
HP 10bII+ I/YR = %

23. Discounted cash flows – HP 10bII+
Main keys used in calculations relating to cash flows:
CFj – the cash flow received in period j
CF0 – amount paid up front
CF1 – 1st cash flow received
CF2 – 2nd cash flow received (and so on)
Nj – the number of payments equal to CFj, default value is 1
Enter cash flow, then If this cash flow is received 3 times, for example, then hit 3 then then
NPV – net present value
IRR/YR – internal rate of return
C ALL to clear cash flow register

24. Discounted cash flows – HP 10bII+
Suppose that an initial investment of $1,000 results in the following sequence of annual cash flows:
What is the internal rate of return associated with this investment?
Make sure P/YR = 1
Enter the initial cash flow, -1000, into CF0
Enter the first cash flow, 25, into CFj
Enter the second cash flow, 35, into CFj
Enter the third and final cash flow, 1300, into CFj
Solve for the IRR, %
Period 1 2 3
Cash flow 25 35
1300

25. Discounted cash flows – HP 10bII+
Suppose that an initial investment of $1,000 results in the following sequence of annual cash flows:
What is the net present value associated with this investment if your required return is 10%?
Make sure P/YR = 1
Enter the initial cash flow, -1000, into CF0
Enter the first cash flow, 25, into CFj
Enter the second cash flow, 35, into CFj
Enter the third and final cash flow, 1300, into CFj
Enter into I/YR
Solve for the NPV,
Period 1 2 3
Cash flow 25 35
1300

26. Discounted cash flows – HP 10bII+
Suppose that an initial investment of $5,000 results in a payment $750 a year for 25 years. Make sure P/YR = 1.
What is the IRR of this investment?
Enter the initial cash flow, -5000, into CF0
Enter the cash flow, 750, into CFj
Enter the number of payments, 25, into Nj
Solve for IRR/YR,
What is the net present value associated with this investment if your required return is 12%?
Enter into I/YR
Solve for the NPV,
What is the net present value associated with this investment if your required return is 15%?
Enter into I/YR
Solve for the NPV,

27. Discounted cash flows – HP 10bII+
Suppose that an initial investment of $10,000 results in a payment $750 a year for 100 years. Make sure P/YR = 1.
What is the IRR of this investment?
Enter the initial cash flow, -5000, into CF0
Enter the cash flow, 750, into CFj
Enter the number of payments, 90, into Nj
Enter the number of payments, 10, into Nj
Solve for the IRR,
What is the net present value associated with this investment if your required return is 10%?
Enter into I/YR
Solve for the NPV,

28. Discounted cash flows
Suppose that an initial investment of $2,500 results in the following sequence of annual cash flows:
What is the internal rate of return associated with this investment?
IRR = %
What is the net present value associated with this investment if your required return is 10%?
What is the net present value associated with this investment if your required return is 5%?
Period 1 2 3
Cash flow 60 75
2850

29. Discounted cash flows
Suppose that an initial investment of $7,000 results in a payment $825 a year for 120 years
What is the IRR of this investment?
IRR =
What is the net present value associated with this investment if your required return is 10%?
NPV =
What is the net present value associated with this investment if your required return is 12%?
NPV =