Calculator Keystrokes Flashcards
How to do Weighted average on the calculator?
Question:
Tom Henson would like to know the expected return on his portfolio. He owns 100 shares of ABX Inc. with total current market value of $3,500; 100 shares of KLP with total current market value of $4,200; and 9 BCI bonds with total current market value of $8,500. Tom expects a return of 30.0%, 12.0%, and 9.0%, respectively, on each investment.
Use the INPUT, Σ+, and the Shift 6 Key (xw,b) x for weighted average. We are looking for weighted average of the x variable so make sure to put proper keystrokes in.
Answer:
30 INPUT, 3500 Σ+
12 INPUT, 4200 Σ+
9 INPUT, 8500 Σ+
then Shift 6 (xw,b) to get 14.3148
What is Shift 6?
The weighted average of a series.
What is Shift 7?
Mean return of an asset
What is Shift 8?
Standard Deviation of an group of securities.
College Fund Example
Calculate the college fund required to start a four year college program in 15 years time. The tuition fees are currently 12,000 and are first payable at the start of year 16. Inflation is 4% and the rate of return is 9%. In addition, calculate the lump sum which needs to be invested today to provide the college fund and calculate what is needed on an annual basis.
This problem is solved in three steps.
- Calculate the tuition fees at the start of year 16 allowing for inflation of 4%. (Draw a timeline from 3-18 with n=15 above the line and i=4% below the line) this needs to be solved for FV and calculated in END mode.
- Calculate the total college fund needed at the start of year 16. (Draw a timeline from 18-21 with n=4 above the line and i=[(1.09/1.04) - 1 x 100] = 4.808% below the line) this needs to be solved for FV and calculated in BEG mode.
- Calculate the amount which needs to be invested today to create the college fund. (Draw a timeline from 3-18 with n=15 above the line and i=9% below the line) this needs to be solved for PV or PMT and calculated in END mode.
1. Calculate the Tuition Fees Allowing for Inflation
The current tuition fee is 12,000 (PV), this needs to be compounded at the inflation rate (g) for a period of 15 years (n), to calculate what the fees will be at the start of year 16. The calculation is carried out using the future value of a lump sum formula as follows:
Tuition fees = FV = PV x (1 + g)n
PV = Current tuition fees = 12,000
n = number of years = 15
g = inflation rate = 4%
Solve for Future Value (Doesn’t matter if you are in BEG or END)
FV = Tuition fees = $21,611.32
2. Calculate the Total College Fund Needed
The tuition fees will commence at the start of year 16 at the value calculated in step 1 of $21,611.32, they then continue for a further 3 years increasing each year by the inflation rate of 4%.
The college tuition fees are in fact a four year annuity due growing at the rate of inflation (g). The present value of the 4 year annuity at the start of year 16 is give by the present value of a growing annuity due formula as follows: Use END mode
PMT = tuition fees = 21,611.32 n = number of years = 4 i = nominal rate = [1.09/1.04)-1 = 4.808% PV = $80.677.02 College Fund Needed
3a. Calculate the Amount Invested to Create the College Fund
The final step is to calculate the lump amount which needs to be invested today in order to create the college fund of $80,677.02 by the start of year 16. This is simply a matter of discounting the value of the college fund at the start of year 16 back to the present day using the present value of a lump sum formula.
FV = College fund at start of year 16 = $80,677.02 n = number of years = 15 i = nominal rate = 9% PV = $22,148.91 Lump Sum Needed
3b. Alternative Funding Using an Annuity (END Mode) Not sure why we use end here. Need to better understand why?
As an alternative to the lump sum investment of 22,148.91, a 15 year annuity could be taken out to provide the required college fund at the start of year 16. The annual payments for such an annuity are given by the future value of an annuity formula, and are calculated as follows:
FV = Value of college fund = 80,677.02 n = number of years = 15 i = nominal rate = 9%
PMT = 2,747.77
What is PVAD? BEG or END
Think of PVAD B or pvad b the d and b look alike.
Present Value of An Annuity Due (PVAD)is solved in BEG Mode
We are usually solving for something in the future (BEG). Take present value and inflate it into the FUTURE.
Which direction are you supposed to calculate?
I start at the BEG and calculate FORWARD
What is PVOA? BEG or END
Think of PVOA - The O A an E for END are all vowels.
Present Value of An Oridnary Annuity (PVAO) is solved in END Mode
We are usually solving for something in the past (END). Bring future number back into the past.
Which direction are you supposed to calculate?
I start at the END and calculate RETRO BACK
How do I calculate Mortgage Amortization?
Amortization Problem 1
Here are the keystrokes for the $135,000, 30-year loan with a 4.5% interest rate: Make sure the calculator is in the END mode, 12 P/YR
Keystrokes are
135,000, PV
4.5, I/YR
30, SHIFT, N (should show 360 payments) Solve for PMT = $684.03
Now, without clearing the calculator, let’s take a look at the first payment. The keystrokes are:
1, INPUT
SHIFT, AMORT
Note: The “INPUT “key is found below the “N” key, and “AMORT” is the
alternate function on the “FV” key.
“1-1” should now be on your screen. This tells you that you are looking at the first payment. Now, each time you strike the “=” key, you will see the following:
= -177.78 PRIN (principal paid)
= -506.25 INT (interest paid)
= 134,822.22 BAL (remaining balance)
How do you solve Effective Annual Rate (EAR)?
- 50% compounded monthly
- 50% compounded quarterly
Step 1 - Enter the nominal rate and press Shift, NOM%
(I/YR key)
Step 2 - Enter the number of compounding periods and press
Shift, P/YR (PMT key)
Step 3 - Calculate the effective rate by pressing Shift, EFF%
(PV key).
Monthly Answer
Step 1: 5.50 SHIFT NOM%
Step 2: 12 SHIFT P/YR
Step 3: SHIFT EFF%
Monthly = 5.6408
Quarterly Answer
Step 1: 5.50 SHIFT NOM%
Step 2: 4 SHIFT P/YR
Step 3: SHIFT EFF%
Quarterly = 5.6145
