FIN 335: Time Value of Money Problems
Computed on a Texas Instrument BA II Plus financial calculator
Before you start:
? The calculator comes set to two decimal places.
? The gray [2ND] key activates the functions that appear above the calculator buttons.
Example: Above the PV key, AMORT is written in gray letters. To use it, press 2nd and then press
[PV] = AMORT.
? IMPORTANT: To clear previous work:
Press [2ND] and [FV] CLR TVM (Clear Time Value of Money memory registers).
Another clearing option is to press 2nd and Reset. It will reset the calculator to its original settings.
? Most of the data entry will be value first, then the function. Example: press 4, then press N, the
display will be N = 4.
? Some values MUST be recorded in memory with the ENTER key. Be careful to make sure your
entry has been acknowledged by the calculator. It will say the function you want set to the value
entered. Example: P/Y = 4 or N = 36.
? Payments are cash outflows and may appear as negative (-) depending on the calculator used.
Problem 1: Computing Effective Rates (i.e., the Annual Percentage Rate - APR)
Given: Pay 8% annually, compounded quarterly. What is the effective rate?
Values:
Periods/yr. = 4
Nominal Rate = 8
Calculator:
1. Press [2ND] and then [I/Y] key. Press 4 and then ENTER. It will display: P/Y = 4.00
2. Press [2ND] and then [CPT] key = QUIT. The display will go to 0.
3. Press [2ND] and I CONV (you’ll find it above the number 2).
4. The field NOM will appear. Press 8 and then press ENTER. It will display: NOM = 8.
5. Press the ? key and EFF will display.
6. Press the ? key again and C/Y will display.
7. Press 4 and then ENTER. It will display: C/Y = 4.
8. Press ? key and return to the EFF display.
9. Press CPT and the calculator will return the effective rate of 8.24.
Note: When you press [2ND] and the [I/Y] keys it opens the P/Y and C/Y memory registers. The
display shows P/Y. If you press the ? key, you will see C/Y. When we set the P/Y value, the
calculator automatically sets the C/Y to the same value. In these instructions, we set the P/Y value. 2
Problem 2: Future Value
Given: What is the future value of $1000 invested today at 8% per annum, compounded quarterly over
5 years?
Values:
N = 5 NOTE: Five years covers 20 quarters so the N value is not 5 but 20 (5*4).
PV = 1000
I = 8
P/Y = 4
Calculator:
1. Press [2ND] and [I/Y].
2. P/Y displays. Press 4 and ENTER. Display shows: P/Y = 4.00
3. Press [2ND] and {QUIT}. The display will go to 0.
4. Press 5. Press [2ND] and then xP/Y (it appears above N). “20” will display. Press N again. Make
sure the display reads: N = 20. (The calculator is multiplying the C/Y value of 4 by 5).
5. Press 1000 and then the PV key. The display should appear as: PV = 1000.
6. Press 8 and then the I/Y key. The display should appear as: I/Y = 8.
7. Press the CPT key and then press FV.
8. The calculator will display the answer of $1,485.95
Problem 3: Annuity
An annuity is an accumulation. Examples are IRA and 401(K) programs. The payments will be
negative (-) values; the Future Value will be positive (+), and the Present Value will be zero (0).
Problem:
? You want to retire in 30 years. You are starting to invest in a growth income fund that promises an
ambitious rate of 15%. You can put in $200 per month. How much will you have in 30 years?
Values:
N = 30 NOTE: The payments will be monthly over 30 years: 30*12 = 360. N = 360
P/Y = 12
I/Y = 15
PMT = -200 (Remember payments are negative.)
Calculator: (need to reset P/Y and C/Y values)
1. Press 2nd and then press I/Y. Press 12 and then press ENTER.
2. P/Y = 12.00 in display.
3. Press 2nd and then press QUIT.
4. Press 30. Press 2nd and then xP/Y (it appears over the N button). 360 will appear. Press N.
N = 360 will display.
5. Press 15 and then press I/Y. I/Y = 15 will display.
6. Press 200. Press the +/- key to the left of the = button. This will change the sign of the 200 from
positive to negative. The display should be -200. Next press PMT. The display will be PMT = -
200.
7. Press CPT and press FV. The answer displayed will be $1,384,655.92. 3
Special Case of an Annuity: Amortization
An amortization is a payment to pay down a loan that has been made in the present.
Problem:
You have an opportunity to take on a 30 year $100,000 mortgage at 7.5% interest. What will your
monthly payments be?
Values:
N = 30 NOTE: The payments will be monthly over 30 years: 30*12 = 360. N = 360
P/Y = 12
I/Y = 7.5
PV = 100,000
Calculator:
1. Press 2nd then press CLR TVM to clear out data from previous problems.
2. Press 2nd and then press I/Y. Press 12 and then press ENTER.
3. P/Y = 12 in display.
4. Press 2nd and then press QUIT.
5. Press 30. Press 2nd and then xP/Y (it appears over the N button). 360 will appear. Press N.
N = 360 will display.
6. Press 7.5 and then press I/Y. The display will be I/Y = 7.5.
7. Press 100,000 and then press PV.
8. Press CPT and then press PMT. The payment displayed will be -$699.21.