Financial Math

Question 1

What is the FV formula?

Answer 1

FV = PV x (1+i)^n

Question 2

What is the FVA formula?

Answer 2

FVA = PMT x [(1+i)^n -1]/i

Question 3

What is the PV formula?

Answer 3

PV = FV/(1+i)^n

Question 4

What is the PVA formula?

Answer 4

PVA = PMT x [1-(1+i)^-n]/i

Question 5

What is the NPV formula?

Answer 5

NPV = CF0 + CF1/(1+k)^1 + CF2/(1+k)^2 + CF3/(1+k)^3… Where k = discount rate

Question 6

What is IRR?

Answer 6

Internal Rate of Return is the rate which sets the NPV equal to zero.

If the IRR is greater than the cost of your capital (discount rate), then the investment will be wealth enhancing, so a rational investor would select it.

Question 7

What should you remember about compounding?

Answer 7

1. The greater the number of compounding periods, the greater the amount of interest, and thus the greater the ending value.
2. The more frequently the compounding, the greater the amount of interest, and thus the greater the ending value.

Question 8

What is the stated interest rate?

Answer 8

Nominal annual rate or the contractual rate.

Question 9

What is the periodic rate?

Answer 9

Rate of interest earned over 1 compound period

Question 10

What is the effective annual rate?

Answer 10

Rate of return actually being earned after adjustments for compounding frequency.

EAR = (1+ i/n)^n - 1

Question 11

What is the formula for simple annualized return?

Answer 11

Simple annualized return = HPR x (365/#)

Question 12

What is the formula for the compound annualized return?

Answer 12

Compound annualized return = (1 + HPR)^(365/#) -1

Question 13

What is the real rate of return?

Answer 13

The nominal rate less the expected inflation rate.

Nominal = (1+Real Rate)(1+Inflation) - 1

Note - when calculating the after-tax real rate of return, calculate the nominal rate after tax, THEN subtract the expected inflation rate.

Question 14

How to calculate the after-tax rate of return?

Answer 14

After Tax Rate of Return = (Pre-Tax Rate of Return)(1 - Marginal Tax Rate)

Question 15

How to calculate the arithmetic rate of return?

Answer 15

[∑(R1)+(R2)+(R3)+(R4)]/n

Question 16

How to calculate the geometric rate of return?

Answer 16

Also known as the Time Weighted Rate of Return [(1+HPR1)(1+HPR2)…(1+HPRn)]^(1/n) - 1

Question 17

What is the formula for the Dividend Discount Model to calculate the price of a stock?

Answer 17

P0 = D1/(r-g)

Where:

D1 = next year dividend payout

r = required rate of return g = dividend growth rate

Question 18

How to calculate the dividend growth rate?

Answer 18

g = (1-Dividend Payout)(ROE)

Question 19

How to calculate the required rate of return?

Answer 19

r = Rf + BETA(Rm-Rf)

Question 20

Formula for Standard Deviation

Answer 20

SD = [∑(probability)(Actual-expected return)^2]^(1/2)

Question 21

How to calculate the current yield for both stocks and bonds.

Answer 21

Current Dividend Yield = (Dividend/Current Market Price) x 100

Current Yield to Maturity for Bonds = (Coupon in $/Current Market Price) x 100

Question 22

What is the difference between the clean price and dirty price of a bond?

Answer 22

Clean price is the price without accrued interest

Dirty Price = Clean Price + Accrued Interest

Question 23

How to calculate the Price Paid for a Mutual Fund with a Front End Load

Answer 23

Price Paid = NAVPS/(1- %Sales charge)

Question 24

How to calculate the Price Received for a Mutual Fund with a deferred sales charge or back-end load

Answer 24

Price Received = NAVPS x (1 - % Redemption Fee)

Question 25

What is the formula for the Price/Earnings ratio?

Answer 25

P/E = Dividend Payout/(r-g)

Where Dividend Payout = Dividend per Share/EPS

Question 26

How to adjust nominal return for inflation?

Answer 26

[(1 + real return)(1 + inflation) - 1] x 100