chapter 5 flashcards
what is Future Value?
the amount to which a present value will grow after earning interest
there are two kinds of interest that money can earn?
- simple interest
- compound interest
what is Simple Interest?
interest is arened only on the original investment and no interest is earned on interest
what is Compound Interest?
interest is earned on interest
Interest Earned Per Year
formula
previous years balance x interest rate
the formula for the future value of I dollars at r% interest per period for T periods is…
FV=I x (1+r)t
how do we calculate Present Value
formula
future values after t periods / (1+r)t
r= discount rate (interest rate used to compute present values of future cash flows)
how do we write the Present Value formula if their a discount factor ?
formula
future payment x 1/(1+r)t
the discount factor measures the present value of $1 to be received in t years from today at a discount rate of r%
how do you know which Present Value options are better at the present ?
for the buyer, the option where they have to pay less would be better. the opposite goes for the dealer, the option with more money would be best
what is a Annuity ?
equally spaced, and level stream of cash flows
ex: loan payments for automobiles, home mortgage
what is a Perpetutiy?
stream level of cash payments that never ends (infinite period)
how do we value Perpetuties?
- the PV of a perpetuity is calculated b y dividing the level cash flow (C) by the interest rate (r)
- cash payment from perpetuity = interest rate x present value
C= r x PV - Present value of perpetuity = Cash Payment / interest rate
how do we calculate PV of t-period annuity?
formula
C x [1/r - 1/r(1+r)t]
how do we calculate FV of t-period annuity ?
formula
C [(1+r)t - 1 / r]
whats the difference between a t-year ordinary annuity and a t-year annuity due ?
- t-year Ordinary Annuity: when you don’t have an immediate payment, but you pay for t-years
- t-year Annuity Due: you start with an immediate payment + the rest of the year you have to pay
what is Growing Perpetutity?
an INFINTIE stream of cash flows growing at a constant rate
what is Growing Annuity ?
a FINITE stream of cash flows growing at a constant rate
whats the formula for PV at a growing perpetuity?
formula
[C1 / r-g]
C1= payment to occur at the end of the first period
r=discount rate
g=growth rate of the payments
what is the formula for PV of growing annuity ?
formula
C1 / r-g (1 - [1+g/1+r]t)
C1= payment to occur at the end of the first period
r=discount rate
g=growth of the payments
t=the number of payments
what is Inflation?
rate at which prices as a whole are increasing
what is Nominal Interest Rate?
rate at which money invested grows
what is Real Interest Rate?
rate at which the purchasing power of an investment increases
how do we calculate the real rate of interest ?
formula
1+real rate=1+nominal rate/1+inflation rate
OR
real rate of interest=nominal rate of interest - inflation rate
what is Effective Annual Interest Rate(EAR)?
interest rate that is annualized using compound interest
what is Annual Percentage Rate (APR)?
interest rate that is annualized using simple interest
what is the formula for EAR?
(m is the number of compounding per year)
EAR= {1 + APR/m}m - 1
