[3] Financial Calculus

Question 1

o -> x
o <- x

Answer 1

Capitalization (+i)
Discounting (-i)

Question 2

Simple interest

Answer 2

-C0, every year take r*C0

Cn = C0*(1+nr)

Question 3

Compound interest

Answer 3

-C0, every year take 0

Cn = C0*(1+r)^n

Question 4

Get the nominal rate

Answer 4

(1+rn) = (1+rr)(1+ri)

rn - nominal rate
rr - real rate
ri - interest rate
(1+ri) - interest

take into consideration the rr if we cannot predict the inflation

Question 5

Effective annual rate

Answer 5

EAR = (1+rn/#compounds)^(#compounds/#k) - 1

Question 6

Annuity

Answer 6

PV = A (1- (1+i)^-n)/i [(1+t)^s]

Question 7

Perpetuity

Answer 7

PV = P/i or PV = P/(i-g)

Question 8

Stock, expected return and present stock price

Answer 8

Stock are shares of individual companies, equity

r = (div1 + p1 - p0)/p0

PV = (div1)/(1+r)^1 + … + (divn + Pn)/(1+r)^n

PV = divn/(r-g)

Question 9

Bond and present bond value

Answer 9

Bonds when company agree to pay interest for money, debt

PV = (jNV)/(1+r)^1 + … + (jNV+NV)/(1+r)^n

jNV is the coupon

Question 10

Yield to maturity (YTM)

Answer 10

Total return anticipated on a bond if the bond is held until it matures, calculated like a bond