Ch. 6 - Future and Present Values of Multiple Cash Flows

Annuity FV Factor =

(Future value factor - 1)/r [(1 + r)^t - 1] / r

Present Value Interest Factor for Annuities

1 - Present Value Factor [1/(1+r)^t]

2 Ways to calculate Future Values

1. Compound accumulated balance forward one year at a time 2. Calculate future value of each cash flow first and then add them up

EAR always ____________ the APR

> Greater than APR

Annuity

A level stream of cash flows for a fixed period of time

Consol

A type of perpetuity, particularly in Canada or the UK

Annuity Due

An annuity for which the cash flows occur at the beginning of the period

Perpetuity

An annuity in which the cash flows continue forever

Annuity Present Value

C * 1 - Present Value Factor ------------------------ r C * 1 - [1 / (1+r)^t] ------------- r

PV for a perpetuity

C/r

Annuities have a _________________________ of payments Perpetuites have a series of cash flows _________________

Fixed, Forever

Time Line

Illustrates process of calculating future value on deposits, written down when they occur. Amount * 1+rate = Balance at end of Year N

Stated Interest Rate

Interest rate expressed in terms of the interest payment made each period. Also known as the "quoted" interest rate

Annuity Due Value =

Ordinary annuity value * (1 + r)

Annuity Due

Series of cash flows in which cash flows occur in the beginning of the period, Must change calculator to BGN for annuity due

Interest-Only Loans

The borrower pays interest each period and pays the principal at some time in the future

Pure Discount Loan

The borrower receives money today and repays a single lump sum at some time in the future

Annual Percentage Rate (APR) =

The interest rate charged per period multiplied by the number of periods per year

Effective annual rate (EAR)

The interest rate expressed as if it were compounded once per year m = num. times interest is compounded

Amortized Loan

The lender may require the borrower to repay parts of the loan amount over time.

Amortizing

The process of providing for a loan to be paid off by regular payments of principal reductions

EAR =

[1 + (Quoted rate/m)]^m - 1

EAR as the q (quoted rate) gets larger=

e^q - 1

Ordinary Annuity

multiple, identical cash flows occurring at the end of each period for a fixed number of periods Ex. Consumer loan payments, lottery payouts, some legal settlements, some investment accounts and retirement payments