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