module 3: interest rates (chapter 5) Flashcards
what is an effective annual rate (ear)?
total amnt of interest earned over a period of one year
if ear = 4.04% and that you invest 10k today, how much will you have after 1 year? 2 years? 6 months?
a) 10k * 1.0404
b) 10k * 1.0404^2
c) 10k * 1.0404^0.5
a bank account pays interest every quarter with an ear of 5%. you plan to make deposits of 1k at the start of every quarter over the next 5 years, with your first deposit today. how much money will you have in your acc after 5 years?
22789
if r is the effective rate for 1 period, then what is the equivalent n-period effective rate?
(1+r)^n - 1
if n > 1, this is an effective rate over more than 1 period
if n < 1, this is an effective rate over a fraction of a period
what do you prefer:
1. bank acc that pays 5% per year (ear) for 3 years
2. bank acc that pays 2.5% every 6 months for 3 years
1) 1.05^3
2) 1.025^6
2!
a bank account pays interest every quarter with an ear of 5%. you plan to make deposits of 1k at the start of every quarter over the next 5 years, with the first deposit today. how much money will you have in your account after 5 years where you increase the amounts that you deposit at a constant rate to 4% per quarter?
33399
does apr take into account the effect of compounding?
ignores it! even if it may occur
if compounding does happen, then in general the apr will not give the correct amount of interest over a year
- cannot simply use apr to calculate pvs or fvs
- need to convert the apr into an effective rate which takes compounding into account correctly
- to convert apr, we need to know the compounding frequency (ann, semiann, month, etc)
what is an annual percentage rate (apr)?
amount of simple interest earned over a 1 year period
how to convert apr with different compounding periods?
ann: (1 + apr/1)^1 -1
semiann: (1 + apr/2)^2 - 1
monthly: (1 + apr/12)^12 - 1
daily: (1 + apr/365)^365 - 1
given an apr with k compounding periods per year the implied effective rate r earned each compounding period is?
r = apr/k
how do you convert an apr to an ear?
ear = (1 + apr/k)^k - 1
what is continuous compounding?
infinite number of compounding periods in a year
how do you find apr given the ear?
apr = ln(1 + ear)
how is the continuously compounded apr denoted as?
rcc
what is the pv of a single cash flow with continuous compounding received T years from now?
pv0 = CTexp(-rcc * T)
if cash flows start immediately at an initial rate of C per year and that this rate increases continuously at the rate gcc, what is the pv if the cash flows are perpetual? annuity?
perpetual:
pv0 = c / (rcc - gcc)
annuity:
pv0 = (c / (rcc - gcc)) [1 - exp(- (rcc - gcc) T)]
where gcc > rcc
what is the fv of a single cash flow that is continuously compounded and invested today?
FV = c0 * exp(rcc * T)
if mackenzie inc receives revenues cont. today at an annual rate of 25 million and this amnt is expected to grow cont. at a rate of 2% (ear) forever and the interest rate is 7% (ear), what is the pv of the firm’s revenue?
c / (rcc - gcc)
rcc = ln(1.07)
gcc = ln(1.02)
25/ln(1.07) - ln(1.02)
xyz comp has operating costs thta will occur cont. over the next 8 years. today these costs are incurred at an annual rate of 4 million. this amnt is expected to grow at a cont. compounded rate of 6% per (ear). what is th epv of these costs, assuming that the appropriate interest rate is 5% (ear, compounded cont.)
pv0 = (c / (rcc - gcc)) [1 - exp(- (rcc - gcc) T)]
= (4 / (ln1.05 - ln1.06)) [1 - exp(- (ln1.05 - ln1.06) 8)]
= 33.24
how do you calculate the required payment on a loan?
- convert quoted apr to appropriate discount rate
- set pv of all remaining payments equal to the outstanding loan balance
- compounding frequency is not stated explicitly but in most cases the compounding frequency is the same as the payment frequency
ex. 3.99% apr for 60 months means an interest rate of .0399/12 = 0.3325% per month with 60 monthly payments
