1. Using the Financial Calculator
Copyright by Diane Scott Docking 2015

2. Copyright by Diane Scott Docking 2015
Learning Objectives
To learn how to use the Financial Calculator
Copyright by Diane Scott Docking 2015

3. TI BA II+ Calculator Setup—Follow This!!
Use one period per year: P/Y = 1
[P/Y] 1
Set decimal to 6 places: Format DEC=6
[FORMAT] 6
Set BGN register to “END”
2ND
ENTER
2ND
ENTER
Copyright by Diane Scott Docking 2015

4. Financial Calculators—TI BA II+
I/Y
PMT FV PV
Number of time periods
Interest rate (%)
Future Value
Present Value
Payment
Basic Calculator Keys
Copyright by Diane Scott Docking 2015

5. Financial Calculators—TI BA II+
Has embedded formulas
Five time value keys: N, I/Y, PV, PMT, FV
Use either four or five keys
Interest rate (I/Y) is entered as a whole number, not a decimal (e.g. 7% is entered as 7)
PV and FV must carry opposite signs (‘+’ or ‘-’)
PMT must carry the same sign as either the PV or the FV, whichever is appropriate
Some calculators distinguish between inflows and outflows
Cash flow sign convention: If a PV is entered as negative the computed FV is positive
Copyright by Diane Scott Docking 2015

6. Copyright by Diane Scott Docking 2015
Time is Money
$100 in your hand today is worth more or less than $100 in one year?
Money earns interest
The higher the interest rate, the faster your money grows
Q: How much would $1,000 promised in one year be worth today if you could be earning 12% interest?
Copyright by Diane Scott Docking 2015

7. Copyright by Diane Scott Docking 2015
Time is Money t0 t1
$1,000 PV
𝑷𝑽 × (𝟏.𝟏𝟐) 𝟏 =$𝟏,𝟎𝟎𝟎 So
𝑷𝑽= $𝟏,𝟎𝟎𝟎 (𝟏.𝟏𝟐) 𝟏
A: $1,000/(1.12)1 = $892.86
Verify: $ x .12 = $ interest earned
plus initial investment = $
yields = $1,000.00
Copyright by Diane Scott Docking 2015

8. Financial Calculators & Cash Flow Sign Convention
Here are the key strokes:
1000 12 1
PV will be NEGATIVE. A -$ But answer is $
By convention we put PV in as a negative number, so that FV will be positive.
Ignore the negative sign. The negative sign simply means you invested (had a cash outflow). FV
Input $1,000 FV
Input 12 I/Y
Input 1 N
Input 0 PMT
Calculate PV (Cpt PV)
Is PV positive or negative?
Why?
What’s the deal?
I/Y N
PMT
CPT PV
Copyright by Diane Scott Docking 2015

9. Copyright by Diane Scott Docking 2015
1. FV of a Lump Sum: What’s the FV of an initial $100 investment after 3 years if i = 10%? 1 2 3
10%
100
FV = ?
$100 x .10 = Interest $ Principal $100
Balance $110 x .10 = interest $11
balance $110
Balance $121 x .10 = interest $ 12.10
balance $121.00
FV = $133.10
$100 x .10 = $10 x 3 yrs. = $30 in interest if withdraw interest each year.
Copyright by Diane Scott Docking 2015

10. Financial Calculator Input: FV of a Lump Sum
Here are the key strokes:
100 10 3
FV will be a POSITIVE $
By convention we put PV in as a negative number, so that FV will be positive.
+│─ PV
Input -$100 PV
Input 10 I/Y
Input 3 N
Input 0 PMT
Calculate FV (Cpt FV)
Is FV positive or negative?
Why?
What’s the deal?
I/Y N
PMT
CPT FV
Copyright by Diane Scott Docking 2015

11. Another Example: FV of a Lump Sum
Mary invests $1,000 today for 20 8%. How much will she have in 20 years?
FVn = PV(1+i) n FV20 = $1,000 (1.08)20 = $4,660.96
Here are the key strokes:
1000 8 20
FV will be a POSITIVE $4,660.96
By convention we put PV in as a negative number, so that FV will be positive.
Input -$1000 PV
Input 8 I/Y
Input 20 N
Input 0 PMT
Calculate FV (Cpt FV)
+│─ PV
I/Y N
PMT
CPT FV
Copyright by Diane Scott Docking 2015

12. Copyright by Diane Scott Docking 2015
2. PV of a Lump Sum: What’s the PV if i = 10% to end up with FV = $100 after 3 years? 1 2 3
10%
75.13
FV = 100
$100 /(1.10)3 = $75.13
Verify:
$75.13 x .10 = Interest $ Principal $75.13
Balance $82.64 x .10 = interest $ 8.26
balance $82.64
Balance $90.90 x .10 = interest $ 9.09
balance $90.90
FV = $99.99 = $100
Copyright by Diane Scott Docking 2015

13. Financial Calculator Input: PV of a Lump Sum
Here are the key strokes:
100 10 3
PV will be a NEGATIVE $75.13.
Ignore negative sign. Answer is $75.13. FV
Input $100 FV
Input 10 I/Y
Input 3 N
Input 0 PMT
Calculate PV (Cpt PV)
I/Y N
PMT
CPT PV
Copyright by Diane Scott Docking 2015

14. Copyright by Diane Scott Docking 2015
3. FV of an annuity Example 1: What is the FV of a 3-year ordinary annuity of $100 at 10%? 1 2 3
10%
10%
10%
$100
100
100
100(1.10)=
110
FV =
100(1.10)2=
121
$331
Copyright by Diane Scott Docking 2015

15. Financial Calculator Input: FV of an ordinary annuity
Here are the key strokes: 10 3
100
FV will be a NEGATIVE $331. Ignore negative sign. Answer: $331.
Cannot put 0 in as a negative.
Input $0 PV
Input 10 I/Y
Input 3 N
Input $100 PMT
Calculate FV (Cpt FV) PV
I/Y N
PMT
CPT FV
Copyright by Diane Scott Docking 2015

16. Example 2: What’s the FV of a 3-year annuity due of $100 at 10%?1 2 3
10%
$100
100
100
110
100(1.10)=
FV =
121
100(1.10)2=
100(1.10)3=
133.10
$364.10
Copyright by Diane Scott Docking 2015

17. Financial Calculator Input: FV of an annuity due
Here are the key strokes:
[BGN] [SET] 10 3
100
FV will be a NEGATIVE $ Ignore negative sign. Answer: $
Cannot put 0 in as a negative.
Set calculator to BGN mode
Input $0 PV
Input 10 I/Y
Input 3 N
Input $100 PMT
Calculate FV (Cpt FV)
2ND
2ND PV
I/Y N
PMT
CPT FV
Copyright by Diane Scott Docking 2015

18. Copyright by Diane Scott Docking 2015
4. PV of an annuity Example 1: What’s the PV of an 3-year ordinary annuity of $100 per year at 10%? 1 2 3
10%
100
100
100
90.91
=100/(1.10)1
82.64
=100/(1.10)2
75.13
=100/(1.10)3
$248.68
= PV
Copyright by Diane Scott Docking 2015

19. Financial Calculator Input: PV of an ordinary annuity
Here are the key strokes:
[BGN] [SET] 10 3
100
PV will be a NEGATIVE $ Ignore negative sign. Answer: $
Cannot put 0 in as a negative.
Reset calculator to END mode
Input $0 FV
Input 10 I/Y
Input 3 N
Input $100 PMT
Calculate PV (Cpt PV)
2ND
2ND FV
I/Y N
PMT
CPT PV
Copyright by Diane Scott Docking 2015

20. Copyright by Diane Scott Docking 2015
Example 2: What’s the PV of an 3-year annuity due of $100 per year at 10%?
100 1 2 3
10%
=100/(1.10)
90.91
82.64
=100/(1.10)2
= PV
273.55
Copyright by Diane Scott Docking 2015

21. Financial Calculator Input: PV of an annuity due
Here are the key strokes:
[BGN] [SET] 10 3
100
PV will be a NEGATIVE $ Ignore negative sign. Answer: $273.55
Cannot put 0 in as a negative.
Reset calculator back to BGN mode
Input $0 FV
Input 10 I/Y
Input 3 N
Input $100 PMT
Calculate PV (Cpt PV)
2ND
2ND FV
I/Y N
PMT
CPT PV
Copyright by Diane Scott Docking 2015

22. Using Calculator for Uneven CFs
Example: What is the FV of this uneven cash flow stream if rates are 10% and payment is made at end of the year? 1 2 3 4
10%
100
300
300
-50
330
300 x (1.10) =
363
300 x (1.10)2 =
133.10
100 x (1.10)3=
FV = $776.10
Copyright by Diane Scott Docking 2015

23. Financial Calculator Input: FV of uneven cash flows
Here are the key strokes:
[BGN] [SET]
, C01 appears,
,F01 appears, ,C02 appears
,F02 appears, ,C03 appears
,F03 appears, ,C04 appears
,F04 appears, ,
C05 appears
, I= appears, , NPV= appears,
NPV = appears. This is the PV of the CFs.
Continued>>>>>>>>>>>
Reset calculator to END mode
Input $0 CF0
Input $100 CF1
Input $300 CF2
Input $300 CF3
Input -$50 CF4
Input 10% interest
Calculate FV
2ND
2ND CF
ENTER ↓
ENTER ↓
ENTER ↓
ENTER ↓
ENTER ↓
ENTER ↓
ENTER ↓
+│─
ENTER ↓
ENTER ↓
NPV
ENTER ↓
CPT
Copyright by Diane Scott Docking 2015

24. Financial Calculator Input: FV of uneven cash flows (continued)
Here are the key strokes:
530.09 10 4
FV will be a $
Input $ PV
Input 10 I/Y
Input 4 N
Input $0 PMT
Calculate FV (Cpt FV) PV
+│─
I/Y N
PMT
CPT FV
Copyright by Diane Scott Docking 2015

25. Copyright by Diane Scott Docking 2015
Example: What is the PV of this uneven cash flow stream if rates are 10% and payment is made at the end of the year? 1 2 3 4
10%
100
300
300
-50
90.91
=100/(1.10)
247.93
=300/(1.10)2
225.39
=300/(1.10)3
______
-34.15
=-50/(1.10)4
$ = PV
Copyright by Diane Scott Docking 2015

26. Financial Calculator Input: PV of uneven cash flows
Here are the key strokes:
[BGN] [SET]
, C01 appears,
,F01 appears, ,C02 appears
,F02 appears, ,C03 appears
,F03 appears, ,C04 appears
,F04 appears, ,
C05 appears
, I= appears, , NPV= appears,
NPV = appears. This is the PV of the CFs.
Reset calculator to END mode
Input $0 CF0
Input $100 CF1
Input $300 CF2
Input $300 CF3
Input -$50 CF4
Input 10% interest
Calculate PV
2ND
2ND CF
ENTER ↓
ENTER ↓
ENTER ↓
ENTER ↓
ENTER ↓
ENTER ↓
ENTER ↓
+│─
ENTER ↓
ENTER ↓
NPV
ENTER ↓
CPT
Copyright by Diane Scott Docking 2015

27. Copyright by Diane Scott Docking 2015
Example: PV of Monthly Uneven Cash
Flow Stream
Agree to make “step payments” on a contract as follows:
$1,000 per month for the first year
$1,300 per month for the second year
$2,000 per month for the third year
At 10% annual rate, what is the PV of these payments?
Copyright by Diane Scott Docking 2015

28. Copyright by Diane Scott Docking 2015
Financial Calculator Input:
PV of Monthly Uneven Cash Flow Stream
Here are the key strokes:
[CLR WORK]
, C01 appears,
,F01 appears, ,C02 appears
,F02 appears, ,C03 appears
,F03 appears, ,C04 appears
, I= appears, , I= appears
, NPV= appears,
NPV = 43, appears. This is the PV of the CFs.
Make sure calculator is set to END mode
Input $0 CF0
Input $1000 CF1-12
Input $1300 CF13-24
Input $2000 CF25-36
Input 10%/12 = % interest
Calculate PV
2ND CF
2ND CF
ENTER ↓
ENTER ↓
ENTER ↓
ENTER ↓
ENTER ↓ ↓
ENTER ↓
ENTER
NPV ÷ =
ENTER ↓
CPT
Copyright by Diane Scott Docking 2015

29. Calculating Effective Annual Rates with a Calculator
Recall the formula:
We can use the Financial Calculator to solve for EAR.
Where: m is number of compounding periods per year.
Copyright by Diane Scott Docking 2015

30. Copyright by Diane Scott Docking 2015
Example: EAR% for a nominal rate of 8%, compounded quarterly? Daily? TO
PRESS
Display
Select Interest Conversion
[ICONV]
NOM =
Enter nominal interest rate 8
8.00
Enter # of compounding periods per year 4
C/Y =
4.00
Compute EAR
EFF =
8.243%
365
365.00
8.3278%
2ND
ENTER ↓ ↓
ENTER ↑
CPT ↑ ↑
ENTER ↑
CPT
Copyright by Diane Scott Docking 2015

31. Copyright by Diane Scott Docking 2015
Example: EAR% for a nominal rate of 10%, compounded semi-annually, quarterly, monthly, and daily? TO
PRESS
Display
Select Interest Conversion
[ICONV]
NOM =
Enter nominal interest rate 10
10.00
Enter # of compounding periods per year 2
C/Y =
2.00
Compute EAR
EFF =
10.25% 4
4.00
10.381% 12
12.00
10.471%
365
365.00
10.516%
2ND
ENTER ↓ ↓
ENTER ↑
CPT ↑ ↑
ENTER ↑
CPT ↑ ↑
ENTER ↑
CPT ↑ ↑
ENTER ↑
CPT
Copyright by Diane Scott Docking 2015

32. Finding “n” and “i” of a Lump Sum
It is EASY to find “n” and “i” using a Financial Calculator
FV & PV of a lump sum:
Example 1: At what interest rate would you have to invest $100 today to end up with $ in 3 years?
Here are the key strokes:
100
133.10 3
I/Y = 10% PV
Input - $100 PV
Input $ FV
Input 3 N
Input $0 PMT
Calculate I/Y (Cpt I/Y)
+│─ FV N
PMT
CPT
I/Y
Copyright by Diane Scott Docking 2015

33. Finding “n” and “i” of a Lump Sum
FV & PV of a lump sum:
Example 2: If you invest $100 today at 10%, how long will it take to grow to $133.10?
Here are the key strokes:
100
133.10 10
N = 3 years
Input - $100 PV
Input $ FV
Input 10 1/Y
Input $0 PMT
Calculate N (Cpt N) PV
+│─ FV
I/Y
PMT
CPT N
Copyright by Diane Scott Docking 2015

34. Finding “n”, “i”, and “payment” of Annuities
It is EASY to find “n”, “i”, and “payments” using a financial calculator.
FV & PV of an ordinary annuity:
Example 1: At what interest rate would you have to invest $100 payments made annually (at end of year) to end up with $331 in 3 years?
Example 2: If you invest $100 annually (at end of year) at 10%, for how many years must you invest before your future value equals $331?
Example 3: How much must you invest annually (at end of year) at 10%, for 3 years to accumulate a future value of $331 at the end of 3 years?
Copyright by Diane Scott Docking 2015

35. Finding “n”, “i”, and “payment” of Annuities
Finding “i”
FV & PV of an ordinary annuity:
Example 1: At what interest rate would you have to invest $100 payments made annually (at end of year) to end up with $331 in 3 years?
Here are the key strokes:
331 3
100
I/Y = 10%
Input $0 PV
Input - $331 FV
Input 3 N
Input $100 PMT
Calculate I/Y (Cpt I/Y)
Need to make FV or payments negative. PV
+│─ FV N
PMT
CPT
I/Y
Copyright by Diane Scott Docking 2015

36. Finding “n”, “i”, and “payment” of Annuities
FV & PV of an ordinary annuity:
Example 2: If you invest $100 annually (at end of year) at 10%, for how many years must you invest before your future value equals $331?
Here are the key strokes:
331 10
100
N = 3 years
Input $0 PV
Input $331 FV
Input 10 1/Y
Input -$100 PMT
Calculate N (Cpt N) PV FV
I/Y
+│─
PMT
CPT N
Copyright by Diane Scott Docking 2015

37. Finding “n”, “i”, and “payment” of Annuities
Finding “payment”
FV & PV of an ordinary annuity:
Example 3: How much must you invest annually (at end of year) at 10%, for 3 years to accumulate a future value of $331 at the end of 3 years?
Here are the key strokes:
331 10 3
Pmt = -$100
Input $0 PV
Input $331 FV
Input 10 1/Y
Input 3 N
Calculate Pmt (Cpt Pmt) PV FV
I/Y N
CPT
PMT
Copyright by Diane Scott Docking 2015

38. Finding “n”, “i”, and “payment” of Annuities
It is EASY to find “n”, “i”, and “payments” using a financial calculator.
FV & PV of an annuity due:
Example 1: At what interest rate would you have to invest $100 payments made annually (at beginning of year) to end up with $ in 3 years?
Example 2: If you invest $100 annually (at beginning of year) at 10%, for how many years must you invest before your future value equals $364.10?
Example 3: How much must you invest annually (at beginning of year) at 10%, for 3 years to accumulate a future value of $ at the end of 3 years?
Copyright by Diane Scott Docking 2015

39. Finding “n”, “i”, and “payment” of Annuities
Finding “i”
FV & PV of an annuity due:
Example 1: At what interest rate would you have to invest $100 payments made annually (at beginning of year) to end up with $ in 3 years?
Here are the key strokes:
[BGN] [SET]
364.10 3
100
I/Y = 10%
Set calculator to BGN mode
Input $0 PV
Input -$ FV
Input 3 N
Input $100 PMT
Calculate I/Y (Cpt I/Y)
2ND
2ND PV
+│─ FV N
PMT
CPT
I/Y
Copyright by Diane Scott Docking 2015

40. Finding “n”, “i”, and “payment” of Annuities
FV & PV of an annuity due:
Example 2: If you invest $100 annually (at beginning of year) at 10%, for how many years must you invest before your future value equals $364.10?
Here are the key strokes:
Already at BGN
364.10 10
100
N = 3
Set calculator to BGN mode
Input $0 PV
Input -$ FV
Input 10 I/Y
Input $100 PMT
Calculate N (Cpt N) PV
+│─ FV
I/Y
PMT
CPT N
Copyright by Diane Scott Docking 2015

41. Finding “n”, “i”, and “payment” of Annuities
Finding “payment”
FV & PV of an annuity due:
Example 3: How much must you invest annually (at beginning of year) at 10%, for 3 years to accumulate a future value of $ at the end of 3 years?
Here are the key strokes:
Already at BGN
364.10 10 3
PMT = $100
Set calculator to BGN mode
Input $0 PV
Input -$ FV
Input 10 I/Y
Input 3 N
Calculate Pmt (Cpt Pmt) PV
+│─ FV
I/Y N
CPT
PMT
Copyright by Diane Scott Docking 2015

42. Constructing Amortization Schedules using the Financial Calculator
Construct an amortization schedule
for a $1,000, 10% annual rate loan
with 3 equal payments in arrears (paid at end of year).
Copyright by Diane Scott Docking 2015

43. Step 1: Find the required payments.
Amortization Schedule Using Calculator
Step 1: Find the required payments. 1 2 3
10%
-1,000
PMT
PMT
PMT
INPUTS N
I/Y PV
PMT FV
OUTPUT
402.11
Copyright by Diane Scott Docking 2015

44. Copyright by Diane Scott Docking 2015
Amortization Schedule using Calculator
2nd AMORT: 1 1
P1 = ___ P2 = ___
BAL = _______ PRN =______ INT =______
enter
enter
Ignore negative sign
302.11
100.00 2 2
enter
enter
69.79
332.33 3 3
enter
enter
365.56
36.56
Copyright by Diane Scott Docking 2015

45. Copyright by Diane Scott Docking 2015
Amortization Schedule using Calculator
BEG PRN END
YR BAL PMT INT PMT BAL
1 $1,000 $ $100 $ $697.89
TOT 1, ,000
Copyright by Diane Scott Docking 2015

46. Copyright by Diane Scott Docking 2015
Example: Amortization of a Real-World Mortgage (and why to stay home with mom and dad)
Buy a $300,000 house with 20% down
Finance $240,000 at 6% over 30 years
Questions:
What are your monthly mortgage payments?
For the first year, how much did you pay in interest and principal?
What is the loan balance at the end of year 5?
For the 12th monthly payment, how much did you pay in interest and principal?
How much total interest did you pay in years 1 through 5?
Copyright by Diane Scott Docking 2015

47. Example: Amortization of a Real-World Mortgage
Questions:
What are your monthly mortgage payments?
N = 30 yrs x 12 = 360 payments
I/Y = 6%/12 = 0.50% ,
INPUTS N
I/Y PV
PMT FV
OUTPUT
1,438.92
Copyright by Diane Scott Docking 2015

48. Example: Amortization of a Real-World Mortgage
Questions:
For the first year, how much did you pay in interest and principal?
Keep payment information in calculator.
2nd AMORT:
P1 = ___ P2 = ___
BAL = ___________
PRN =___________
INT =____________ 1 12
enter
enter
-237,052.77
Ignore negative sign
2,947.23
14,319.83
Copyright by Diane Scott Docking 2015

49. Example: Amortization of a Real-World Mortgage
Questions:
What is the loan balance at the end of year 5?
Keeping everything the same in the calculator
Bring back up to P1 by hitting the ↑ two times.
P1 = ___ P2 = ___
BAL = ___________ 60
enter 60
enter
Ignore negative sign
-223,330.46
Copyright by Diane Scott Docking 2015

50. Example: Amortization of a Real-World Mortgage
Questions:
For the 12th monthly payment, how much did you pay in interest and principal?
Keeping everything the same in the calculator
Bring back up to P1 by hitting the ↑ four times.:
P1 = ___ P2 = ___
BAL = ___________
PRN =___________
INT =____________ 12 12
enter
enter
-237,052.77
Ignore negative sign
252.40
1,186.53
Copyright by Diane Scott Docking 2015

51. Example: Amortization of a Real-World Mortgage
Questions:
How much total interest did you pay in years 1 through 5?
Keeping everything the same in the calculator
Bring back up to P1 by hitting the ↑ four times.:
P1 = ___ P2 = ___
BAL = ___________
PRN =___________
INT = ____________ 1 60
enter
enter
-223,330.46
Ignore negative sign
16,669.54
69,665.73
Copyright by Diane Scott Docking 2015