# Principles of Banking and Finance

**Topics:**Time, Time value of money, Mathematical finance

**Pages:**2 (268 words)

**Published:**April 17, 2013

Single Cashflow

1. Present Value (PV)

* the value on a given date of a payment or series of payments made at other times (past or future) * Discounting from the future

* Value at t=0 on a given time line (“t” is the period, ranging from 0 to n where “n” being the last period). * Net Present Value (NPV): PV after deducting all the costs 2. Future Value (FV)

* The amount to which a specific sum and /or series of payments will grow on a given date in the future * Compounding (interests upon interests)

* Value at t>0 on a given time line

Single Cashflow: Formulas

FV = PV(1 + i)t

PV = FV / (1+i)t

i = (FV / PV)1/t – 1

Effective Interest Rate

* Effective (Annual) Interest Rate (EIR)

* The interest rate expressed as if it were compounded once a year. * Used to compare two alternative investments with different compounding periods * Does not include any fees incurred as part of the loan package * Nominal or Quoted Annual Interest Rate (NIR)

* (periodic rate) x (number of periods per year)

* The rate normally quoted in the loan agreement

* All-in Rate

* NIR that includes all the fees incurred as part of the loan package Formulas: Uneven Cashflow

Even Cashflow

* Annuity – series of equal payments (“PMT”) that occur at regular intervals for a period of time (“t”). * Payment is normally made at the end of the period. For payment occurs at the beginning of the period, it is Annuity Due. Perpetuity – infinite series of equal payments

Formula: Annuities

Formula: Perpetuities

When n → ∞, PV (Perpetuity) = PMT/i

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