FNCE - Notes PDF

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FNCE - Notes...

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Future Value Present Value Period Interest Rate

Formula/Equation FV PV r

Calculator BA-II Plus FV PV I/Y

(Discount Rate) Number of Periods

(for 5% = 0.05) t

(for 5% = 5) N

Cash Flow Number of Times a given

CF F

cash flow occurs in

(when choose CF)

consecutive years

I

Interest rate

(when choose CF) NPV

Net Present Value

Payments amount (Installments amount) New interest rate during

Formula/Equation

Calculator BA-II Plus

C

PMT

g

period (new r)

Formula/Equation number of times the interest is compounded in a YEAR Annual Percentage Rate Effective Annual Rate

m APR (for 5% = 0.05) EAR (for 5% = 0.05)

Calculator BA-II Plus

Simple interest : interest on principle only Compound interest : interest on principle and future interest Multiple Cash Flows : it is when you add cash to your previous investment OR you receive different payments at the end of each period. You calculate FV or PV for each period then sum up. (read the example in ppt chapter 6 page 3 & 9)

Annuities: finite series of equal payments that occur at regular intervals Ordinary annuity: If the first payment occurs at the end of the period Annuity due: If the first payment occurs at the beginning of the period If NOT STATED, will consider "ordinary annuity" Growing Annuity: When the interest rate changes in time (read the example in ppt chapter 6 page 48)

Perpetuities : C: payments amount | r: interest infinite series of equal payments (read the example in ppt chapter 6 page 43) Growing Perpetuities : C: payments amount | r: interest | g: new rate When the interest rate changes in time (read the example in ppt chapter 6 page 46)

Effective Annual Rate (EAR) : m: number of times the interest is compounded in a YEAR The actual rate paid (or received) after calculating compounding interest that occurs during the year. Example: Suppose you can earn 1% per month on $1 invested today. What is the APR? 1(12) = 12% How much are you effectively earning? (EAR) FV = 1(1.01)12 = 1.1268 Rate = (1.1268 – 1) / 1 = .1268 = 12.68%

Annual Percentage Rate (APR) : This is the annual rate that is quoted by law. It is based on simple interest. Example: What is the APR if semi-annual rate is 3%? APR = 3% × 2 = 6% Example: What is the APR if monthly rate is 3%? APR = 3% × 12 = 36% Period Rate : When you have APR, and want period rate, you use the same formula and rearrange it.

Example: What is the monthly rate if the APR is 14% with monthly compounding? Period Rate (monthly rate) = = 1.17%

APR from EAR : When you have effective rate, and want APR, you use EAR formula and rearrange it.

example: example: example:

Effective Monthly Rate from EAR: When you have effective rate, and want effective monthly rate:

Mortgage 1- The bank rate is APR based on semi-annual compounding 2- calculate EAR from APR by using m=2 (semi-annual means 2 times a year)

3- calculate effective monthly rate

4- calculate C (or with Calculator: PMT) to get monthly payment amount

Continuous Compounding Sometimes investment or loan use this term

q: is the rate x

e : is like "pi", it has a value = 2.71828 and there is a function in normal calculators (e

What is the effective annual rate of 7% compounded continuously?

EAR = e0.07 – 1 = 0.0725 or 7.25%

)

IMPORTANT NOTES for calculator: -

+/-: o Cash in flow : should be + (usually FV) o Cash out flow : should be – (usually PV)

-

PMT : o if you are paying money, PMT should be MINUS o if you are receiving money, PMT should be +

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make sure the interest rate (r) is for the same period (t) o 8% interest per year = (8% / 12) = 0.6667% per month

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to delete one entered digit, press →

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to clear the calculator, press 2ND CLR WORK (CE|C)

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to calculate PV/FV/n/r: o to assign value to PV/FV/n/r, first enter the amount then press the button. o to calculate value of PV/FV/n/r, press CPT and the button.

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To calculate Multiple Cash Flow (CF): read the example in ppt chapter 6 page 18 o press CF o enter the receive amount for year 0 o press ENTER, press ↓ o for C01: enter receive amount in year 1

o press ENTER, press ↓ o for F01: enter number of times year 1 amount occurs in consecutive years o press ENTER, press ↓ o for C02: enter receive amount in year 2 o press ENTER, press ↓ o for F02: enter number of times year 2 amount occurs in consecutive years o press ENTER o press NPV o for I : enter the interest rate o press ENTER, press ↓ o to compute net present value: press CPT o ALWAYS clear the calculator:

-



press CF, press 2ND, press CLR WORK (CE|C)



press NPV, press 2ND, press CLR WORK (CE|C)

to calculate Annuity: (for Ordinary annuity, installment end of each period) 

enter number of periods, press N



enter interest for that period, press I/Y



enter installment amount, press PMT



press CPT, press PV or FV

-

-

-

to calculate Annuity: (for annuity due, installment beginning of each period) 

press 2ND BGN (PMT)



press 2ND SET (ENTER)



press CE|C



enter number of periods, press N



enter interest for that period, press I/Y



enter installment amount, press PMT



press CPT, press PV or FV



press 2ND BGN (PMT)



press 2ND SET (ENTER)



press CE|C

to calculate installment (PMT): 

enter number of periods, press N



enter interest for that period, press I/Y



enter present value, press PV



press CPT, press PMT

to calculate Effective Annual Rate (EAR) from Annual percentage rate (APR): 

press 2ND ICONV (2) which means interest conversation



In "NOM=" enter the APR



ENTER



↓

-



Leave the "EFF" as it is



↓



In "C/Y" enter the compounding term (semi-annual: 2)



ENTER



↓



↓



when you reach "EFF=" press CPT it shows the effective annual rate

to calculate Loan / Mortgage installment AND principal on … year 

press 2ND P/Y (I/Y)



In "P/Y=" enter the number of payments per year



ENTER



↓



In "C/Y=" enter the compounding term (semi-annual: 2)



ENTER



CE|C



enter the APR for "I/Y"



enter the number of installments for "N" (2 years: 24)



enter the loan amount for "PV"



CPT PMT (you will have monthly installment)

Now, continue to calculate principal amount remaining after 5 years: 

press 2ND AMORT (PV)



In "P1=" enter starting period (from the first installment: 1)



ENTER



↓



In "P2=" enter ending period (at 5 years later: 60)



ENTER



↓



BAL shows the outstanding at the end of period



↓

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PRN shows the total amount you paid for the principal in the period

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↓



INT shows the total amount you paid for the interest in the period...