class 3: future and present values of money Flashcards
nominal interest rate
interest ratebefore takinginflation or compounding into account
Annual Percentage Rate (APR)
nominal interest rate
same as Stated Rate, Quoted Rate or Advertised Rate on a loan
what is the calculation of the APR or nominal interest are)
π΄ππ = ππ‘ β π
ππ‘: rate for the period
π: number of periods
The Effective or Equivalent Annual Rate or EAR
the actual rate you pay
takes into account the fact that we will pay interest on the interest (compounding)
formula for EAR?
EAR = (1 + rt)^n β 1
what are the five variables of the time value of money (TVM)
PV: Present Value
FV: future value
n: number of compounding periods
I: interest rate per period (discount rate)
pmt: payment
future value of money
how much a given amount of money today will be worth at a future date
the amount of money invested today plus the interest that money will earn
what is the formula to find FV (future value of money)
πΉπ = ππ β (1+π)^π
annuity
a fixed sum of money paid to someone each year
how do you calculate the future value of an annuity?
ππ½π¨ = π·π΄π» β ((π+π)^πβπ)/π
FVA = the future value of an annuity stream
PMT = the dollar amount of each annuity payment
r = the interest rate
n = the number of periods in which payments will be made
present value or discounted value?
is how much a given amount of money received on a future date is worth in todayβs dollars
the amount of money that must be invested today to equal the amount of cash received on a future date
what is the formula to find PV (present value)
ππ = πΉπ / (1+π)^π
how do you calculate the present value of an annuity?
π·π½π¨ = π·π΄π» β (πβ(π+π)^βπ) / π
PVA = the present value of an annuity stream
PMT = the dollar amount of each annuity payment
r = the interest rate
n = the number of periods in which payments will be made
how do you calculate present value of annuity if it is received at the beginning of the period?
multiply the PVA by (1 + r)
net present value
Find the present value of the cash flow of your investment
See how much youβre going to spend today
The net present value is the present value of the cash flow β the money spent on investment