BASICS ↓

Interest rate conversion

\( i_2 = \sqrt{(1+i_1)} \)

Is it a capitalization or discounting function?

\( f(t) = \frac{ t }{1+exp{-3x}} \)

Force of interest

\( \delta(t) \)\(= \frac{ f'(t) }{ f(t) } \)
ANNUITIES AND FUNDS ↓

Annuities

\( a_{n,i} \)\(\;=\; \frac{1-(1+ir)^{-t}}{ir} \)

Fund or value at certain time

\( F(3) \)\(= R a_{n,i}+ R s_{n,i'} \)
MATURITIES ↓

Average arithmetic maturity

\( t^A \) =\( \frac{\sum_{t=1}^T tR_t}{\sum_{t=1}^T R_t} \)

Average maturity

\( \Bigl( \sum_{k=1}^{n} R_k \Bigr) \)\( g(avgMat) \)\( = \sum_{k=1}^n R_k g(t_k) \)

Duration

\( D \)\(\;=\; \sum^T \) \( \frac{t \; \cdot \; R_t \cdot (1+ir)^{-t}}{R_t \cdot (1+ir)^{-t}} \)

PROJECT SELECTION ↓

Net present value (VAN/NPV/REA)

\( {NPV \atop REA} = \sum_{t=1}^T \frac{R_t}{(1+i)^t} \)

IRR/TIR

\( \sum_{t=1}^T \frac{R_t}{(1+IRR)^t} = 0 \)

Payback period

\( R1+R2 \ge 0 \) so the Payback period is 2
AMORTIZATION ↓

Simple amortization

Italian amortization