P-P
PAlso add - sign in the end of the programs P and Q below "PV =".
Originally designed for Casio fx-7700GB, some of the later models already have financial programs built-in.
For 1st-generation models such as 7700G use:
finance.txt
For 2nd-generation models such as 9850G use:
finance9850.txt
Financial calculators and spreads sheets use negative number for either PV or FV to show cash flow direction. But the direction seems unimportant. I did not use that.
If PV was positive and FV was also positive, then it means
if the PV
was your money, then the FV is also your money; if the PV was not your money,
then the FV is also not your money. When the signs change, then the right of
the money changes.
* If you want the conventional way showing the directions of cashflows, then
change the program A to "PV"?P
-PP
Also add - sign in the end of the programs P and Q below "PV =".
Without payments
F: Use it when you want future value.
P: Use it when you want present value.
N: Use it when you want n
I: Use it when you want interest rate. It will display percentage.
With payments
M: Use it when you want future value. For future value of annuity, put 0 for
PV, put negative number of the payment. For annuity due, put the payment amount
into PV, put negative number of the payment; when you find the result, subtract
the payment from the result.
Q: Use it when you want present value. For present value of annuity, put 0 for
FV, put positive number of the payment. For annuity due, put the payment into
FV; add the payment into the result.
U: Use it when you have uneven annuity. It finds both the present and future
values. Put 0 for 0th payment in the regular annuity. In annuity
due, start with 0 and put until n-1.
V: Use it when you look for n. Because non-natural number n is impossible, it
finds n and n-1 along with its errors. You should take the one with smaller
error.
W: Everything is the same with V but it is for annuity due.
J: Use it when you look for interest rate. You can also use it to find IRR when
you have equal cash flows. In this case, put the initial investment into PV
as positive, put 0 for FV.
R: Everything is the same with J but it is for annuity due.
Others
K: Use it when you look for IRR. Put positive number for INV
L: Use it when you look for payment.
T: Everything is the same with L but it is for annuity due.
To find NPV
find the present value of cash flows by finding annuity value,
then subtract the initial investment from the result.
For programs J, R, and K, put please put positive number for PV or INV(no 0’s either). Interest rate is not flexible enough to adjust to varying PV, FV and PMT. But you would not have any problems for most of problems. When you see that the calculator is taking too much time, then you should consider it as interest rate is having flexibility problem, thus press AC button to stop the operation.
F, P, I, N, U: The result would come out immediately, because they need less
than 10 calculations.
M, Q, V, W: The result would come out little bit longer, because they need about
10 times the number of N calculations.
J, R, K, L, T: The result would come out much longer, because they need about
100 times the number of N calculations.
Knowing how to select which program in which situation is a very important matter. The following examples would help you know the programs.
Question 1: Jason is going to deposit $1 thousand on January 1, 1998. The interest rate is 9%. How much he would get in January 1, 2003?
What you should do: Select program F, since PV, INT, and N are given in the problem and you are looking for FV. Put 1,000 into PV, 9 into INT, and 5 into N. You would get 1538.623955.
Answer: $1,538.62
Tip: PV is the money before, FV is the money after, INT is interest rate in percentage, N is period.
Question 2: John has borrowed money from the Bank of Globe 5 years ago. The interest rate has been 8%. John has to pay back $2000. How much had he borrowed 5 years ago?
What you should do: Select program P, since FV, INT, and N are given and you are looking for PV. Run program P. Put 2,000 into FV, 8 into INT, 5 into N. You would get 1361.166394.
Answer: $1,361.17
Question 3: Jetson Company is issuing a zero-coupon bond. The price $500. The holders would get $1000 after 10 years. What is the interest rate of the Jetson Company’s bond?
What you should do: Select program I, since FV, PV, and N are given and you are looking for INT. Put 500 into PV, 1000 into FV, and 10 into N. You would get 7.177346254.
Answer: 7.18%
Question 4: Mrs. Jordan is going to deposit $10,000 into the Bank of Internet. She wants to get $20,000. The interest rate is 12%. How many years does she have to wait?
What you should do: Select program N, since PV, FV, and INT are given and you are looking for N. Put 1e4 (which means 1 x 104; e can be put by pressing EXP button) into PV, 2e4 into FV, and 12 into INT. You would get 6.116255374.
Answer: Little more than 6 years, or 6 years and 1 month and 12 days(approximately), or 7 years
Question 5: Jack has been putting $50 every month for 60 months of annuity. The monthly interest rate is 1.1%. How much would he get?
What you should do: Select program M, since you are looking for future value (the after) of annuity. Put 0 into PV, 1.1 into INT, 60 into N, and -50 into PMT. The result is 4217.421221.
Answer: $4,217.42
Question 6: Jill has borrowed $5,000 from the Bank of New Korea 7 years ago. The interest rate is 10%. She has paid $750 every year. How much does she owe now? (She has paid this year’s payment.)
What you should do: Select program M, since you have PV, INT, N, and INT and you are looking for FV. Put 5,000 into PV, 10 into INT, 7 into N, and 750 into PMT. The result is 262.820725.
Answer: $262.82
Question 7: Joel owes $5000 now to the Bank of Ilsan She had been paying $400 every year for 10 years. The interest rate is 13%. How much had she borrowed originally?
What you should do: Select program Q, since you have FV, INT, N, and INT and you are to find PV. Put 5,000 into FV, 13 into INT, 10 into N, and 400 into PMT. The result is 3643.439131.
Answer: $3643.44
Question 8: Mr. Jensen wants to receive $8,000 every year for the next 20 years, and the interest rate is 5%. How much he has to deposit?
What you should do: Select program Q, since this is a question of present value of an annuity. Put 0 into FV, 5 into INT, 20 into N, and 8,000 into PMT. You would get 99697.68274.
Answer: $99,697.68
Question 9: Joan, an employee of the Bank of New Memphis, had visited Kim’s Food’s owner, Mr. Kim for uneven annuity deposit for last 12 months. The monthly interest rate is .9%
|
Jan |
Feb |
Mar |
Apr |
May |
Jun |
Jul |
Aug |
Sep |
Oct |
Nov |
Dec |
|
$500 |
$600 |
$620 |
$620 |
$700 |
$700 |
$800 |
$800 |
$700 |
$600 |
$500 |
$450 |
How much does Mr. Kim have on his account?
What you should do: Select program U, since it is a problem of uneven annuity. Put .9 into INT and 12 into N. Put 0 into 0-th cash flow, then put each cash flow carefully. FV is 7980.400928 and PV is 7166.889617.
Answer: $7,980.40
Question 10: Jean has bought a new model of Sonata from Hyundai dealer at the price of $12,000 on installment program. There was no down payment. She has to pay $399 for 36 months. What is the interest rate?
What you should do: Select program J, since you have PV, FV, N, and PMT. Put 12e3 into PV, 0 into FV, 36 into N, and 399 into PMT. The result would come out in 30 seconds that is 1.0062 (my calculator is fx-7700GB; if you have a better model, you would get faster result. Programs J, R, K, L, and T take a lot of time because it has to make hundreds and thousands of calculations. The calculating time would depend on N. If you have 3 for N, then it would take about 3 seconds).
Answer: 12.07% (it had been multiplied by 12)
Question 11: Julia is borrowing $10,000 from the Bank of New Burner. The interest rate is 6.25%. She has to pay it out in 10 years. How much does she have to pay each year?
What you should do: Select program L, since you have everything except for PMT. Put 1e4 into PV, 0 into FV, 6.25 into INT, and 10 into N. You have 1374.817 in 22 seconds.
Answer: $1,374.82
Question 12: Max Company is investing on Project X that needs the investment of $100,000. The cash flows would be $50,000 in the 1st year, $55,000 in the 2nd year, and $28,000 in the 3rd year. What is the IRR of the project?
What you should do: Select program K, since it is a problem of IRR and the cash flows are uneven. Put 3 into N, 1e5 into INV, 5e4 into 1st CF, 55e3 into 2nd CF, 28e3 into 3rd CF. The result is 17.2646.
Answer: 17.26%
Question 13: Max Company is investing on Project Y that needs the investment of $100,000. The cash flows would be fixed at $20,000 for the next 6 years. What is the IRR?
What you should do: Select program J, since the cash flows are perfectly even. Put 1e5 into PV, 0 into FV, 6 into N, and 2e4 into PMT. The result is 5.4717.
Answer: 5.47%
Question 14: Rex Company is investing on Project Q that needs the investment of $100,000. The cash flows would be $90,000 for the 1st year, $37,000 for the 2nd year, and $1,000 for the 3rd year. The interest rate is 8%. What is the NPV?
What you should do: Select program U, since you need to find PV for the cash flows. Put 8 into INT, 3 into N, -1e5 into 0th CF, 9e4 into 1st CF, 37e3 into 2nd CF, 1e3 into 3rd CF. PV is 15848.70193.
Answer: $15,848.70
Question 15: Rex Company is investing on Project Z that needs the investment of $100,000. The cash flows would be fixed at $25,000 for the next 7 years. The interest rate is 7.5%. What is the NPV?
What you should do: Select program Q, since you need to find PV for the cash inflows first, which is the same as the present value of annuity. Put 0 into FV, 7.5 into INT, 7 into N, 25e3 into PMT. You would get 132415.033 for PV. Subtract the investment from the PV, which is $100,000.
Answer: $32,415.03
Question 16: Jay is buying a piano at the price of $1,800 on installment program. There is no initial payment. The monthly interest rate is 1.1%. He wants to pay $80 each month. How many times does he have to pay?
What you should do: Select program V, since you are looking for N. Put 1800 into PV, 0 into FV, 1.1 into INT, and 80 into PMT. You would get N of 26; N’s error of -0.6120885801 and N-1’s error of 78.52414582. Since you have less error for N, 26 is the reasonable N
Answer: 26 times.