TVM (Interest Rates) Flashcards
What is EAR?
Effective Annual Rate
It indicates the TOTAL amt. of interest earned at the end of one year. It also considers effects of compounding (5% annually is NOT the same as 2.5% every 6 months)
What are interchangeable terms for EAR?
- Effective Annual Yield (EAY)
- Annual Percentage Yield (APY)
What is the formula when ER is asked over a specific amount of time (ex. quarterly, monthly, etc)
= (1+EAR) ^ (1/compounding period) -1
What are the different types of compounding periods/values? List: Daily, Monthly, Quarterly, Semi-annually, Bi-annually,
Daily period: 365
Monthly: 12
Quarterly: 4
Semi-annually: 2
Bi-annually: .0.5
When can ER be applicated?
ER can be used to calculate payments/deposits where capital compounds
What is compounding?
Interest on interest. The core concept is that you earn interest not only on the initial investment (principal) but also on the accumulated interest that has been added to the principal. Longer time = greater impact of compounding.
What is the algebraic calculation of Effective Rates (eg. “How much will you need to save at the end of each month to get $100k in 10 years?)?
C = FV / (1/4) * [(1+rate)^nper - 1]
Rate: From finding interest rate using EAR
NPER: Number of years * amt of months calculated
EX. If calculates quarterly in 10 years = 10 * 4
If monthly = 10 * 12
If semi-anually = 10 * 2
What is the excel formula for Effective Rates?
= PMT(Rate, Nper, PV, FV)
What is APR? What is simple interest?
The Annual Percentage Rate (APR) indicates the amt. of simple interest earned in one year. The APR doesn’t reflect the true amt. over one year; it CANNOT BE USED AS A DISCOUNT RATE and is not an EAR.
Simple interest is the amt. of interest earned w.o the effects of compounding.
THINK: DIVIDE
How do you convert APR to implied effective interest rate other than EAR? Will be denoted by ‘r’
OR
How can you calculate the effective rate for a period (monthly, quarterly)?
r = APR / k
k = compounding periods per year
How do you convert an APR to an ER?
ER= ((1 + APR/k)^k) - 1
How do you go from an Effective Rate to an Effective Rate?
Ex. EAR to EQR?
Do..
= (1+EAR)^(1/4)-1
If a question mentions monthly compounding and asks for FV at 6 (ex.) of years, what should you do to the periods (nper part of =PMT aka how you get the answer)?
Convert any mention of monthly, semi-annually, annual, etc., mentions into periods.
Ex.
72 periods for monthly (126yrs)
12 periods semi (26yrs)
How many months are in a quarter? So for going from EQR to EMR, what would the exponent be? What about EMR to EQR?
3 months in a quarter.
EQR > EMR: 1/4
EMR > EQR: 3
What are the needed variables for PMT, and whats the process on how to get them?
PMT = (rate, nper, pv)
rate = effective compounding rate found through a couple step process
nper = number of periods. can be found by multiplying years * however many months in those years
pv = the amt. of mortgage or loan
What is the formula for EAR after tax?
EAR * (1-tax rate)
