Lecture 7 Flashcards
annuity = ?
a series of equal payments that occur a number of time periods
ordinary annuity = ?
exists when the equal payments occur at the end of each time period
FVA = ?
future value of annuity
PMT = ?
periodic payment in equal amounts
ordinary annuity equation = ?
FVA = PMT x (((1+r) to the power of n - 1) / r)
n = ?
number of periods
r = ?
compound interest rate
annuity due = ?
exists when equal payments start at the beginning of each time period
you want £1000 every year for 3 years at an 8% interest rate
what’s the FVA?
1000 x (((1+0.08) to the power of 3 -1) / 0.08) = 3246.4
PVA = ?
present value of annuity
what is the equation for present value of annuity?
PVA = PMT x ((1-(1/(1+r) to the power of n) / r)
will receive £1000 every year one year from now for 3 years at 8% interest rate
what’s the PVA?
1000 x ((1-(1/(1+0.08) to the power of 3) / 0.08 = 2577.1
interest rates cause the FVA to be…
higher than FVA would be expected to be
interest rates cause the PVA to be…
smaller than PVA would be expected to be
what are the 5 variables for annuity problems?
FV = future value
PV = present value
r = interest rate
n = number of compounding periods
PMT = payment amount
basic equation for compounding more than once a year = ?
FV = PV x (1 + r/m) to the power of n*m
what is the FV of a 2 year, £1000, 8% interest loan with semi-annual compounding?
FV = 1000 x (1+0.08/2) to the power of 2*2 = 1169.86
APR = ?
annual percentage rate
a stated rate determined by multiplying interest rate charged (r)
per period by the number of periods in a year (m)
APR equation = ?
r * m
what’s the APR on a car loan that charges 1% per month?
1% x 12 = 12% APR
how is APR expressed?
as a percentage
EAR = ?
effective annual rate
the opportunity cost measure of the interest rate when compounding occurs more frequently than annually
EAR equation = ?
(1+r) to the power of m - 1
what’s the EAR on a credit card loan with an 18% APR and with monthly payments?
r = 18% / 12 = 0.015
(1+0.015) to the power of 12 - 1 = 19.56%
