Chapter 4: TVM

Question 1

compounding

Answer 1

process of finding the future value of a single or series of payments. it’s based on periodic interest rates unless using continuous compounding

Question 2

cash flows

Answer 2

can be positive or negative

for a borrower, the first cash flow is positive and the rest are negative. opposite for a lender

Question 3

Methods to solve TVM probs

Answer 3

1. step by step approach- using the timeline. helps show you what’s happening but is time consuming
2. formula approach- FV(n) = PV(1 +N) ^N
3. financial calculator
4. spreadsheets

Question 4

simple vs compound interest

Answer 4

• Simple interest: when interest isn’t compounded – interest is earned/charged only on principal not on interest. AKA regular interest. Divide the nominal interest rate by 365 and multiply the # of days funds are borrowed to find the interest for the term borrowed. Fixed % of the principal amount that was borrowed.
• Compound interest- interest earned/charged on principal and interest. Compound accrues and is added to the accumulated interest of previous periods.

Question 5

opportunity cost

Answer 5

rate of return you would earn on an alternative investment of similar risk if you don’t invest in the security under consideration

Question 6

discounting

Answer 6

finding the present value

opposite of compounding

Question 7

perpetuity

Answer 7

payments of a fixed amount that continue indefinetly

Question 8

relationship between PV and IR

Answer 8

If interest rates rise, PV declines

if interest rates fall, PV rises

Question 9

annuity
ordinary/deferred annuity
annuity due

Answer 9

1. series of payments of a fixed amount for a specific # of periods
2. annuity with a fixed # of equal payments happening at the END of each period (mortgages, student loans, car loans, etc)
3. annuity with payments happening at the BEGINNING of each period (rent, life insurance)

Question 10

Why should you rather receive an annuity due for $10,000 per year for 10 years than an otherwise similar ordinary annuity?

Answer 10

Because each payment occurs one period earlier with an annuity due, the payments will all earn interest for one additional year. Therefore, the FV of an annuity due will be greater than that of a similar ordinary annuity.

Question 11

uneven cash flow streams/irregular cash flow streams

Answer 11

cash flows that differ from year to year
-important classes: 1) those where the cash flow stream consists of a series of annuity payments plus an additional final lump sum in year N (ex: bonds) and 2) all other uneven streams (stocks, capital investments)

Question 12

annual compounding

semiannual compounding

Answer 12

1. when interest is compounded once a year
2. when interest is compounded twice a year
   note: most bonds pay interest semiannually, most stocks pay dividends quarterly, most mortgages/student loans/auto loans involve monthly payments and most money fund accounts pay interest daily.

Question 13

types of interest rates

Answer 13

1. nominal annual rates - I (nom)
2. Periodic rates - I(per)
3. Effective annual rates - EAR or EFF%
4. Annual % rates - APR rates

Question 14

nominal annual interest rate

Answer 14

rate quoted by banks, brokers, and other financial institutions. must include the number of compounding periods per year.
For ex: a bank might offer you a CD at 6% compounded daily, while a credit union might offer 6.1% compounded monthly.
NEVER PUT IN A CALC UNLESS IT COMPOUNDS ONLY ONCE A YEAR

Question 15

periodic rate

Answer 15

rate charged by a lender or paid by a borrower each period. It can be a rate per year, semiannually, per quarter, per month, per day, or per any other time interval.
For example: a bank might charge 1.5% per month on its credit card loans, or a finance company might charge 3%
- rate showed on time lines and used in calculations

Question 15

effective annual rate (EAR)

Answer 15

• annual rate that produces the same final result as compounding at the periodic rate for M times per year.
• must be used to compare the effective costs of different loans or rate of return on different investments when payment periods differ

Question 16

annual percentage rate (APR)

Answer 16

nominal annual interest rate actually charged on loans

-important for loans that use add-on interest.

Question 17

what happens to the FV of an investment if interest were compounded some other less-than-annual period?

Answer 17

• because interest is earned on interest more often, expect higher FV the more frequently compounding occurs
• effective annual rate increases with more compounding

Question 18

amortized loan

Answer 18

loan that’s repaid in equal amounts on a monthly, quarterly, or annual basis

Question 18

amortization schedule

growing annuity

Answer 18

payment breakdown with two parts - part interest and part repayment of principal
-series of amounts either received or paid that grow at a constant rate

Question 19

effective rates of return

Answer 19

if you’re comparing costs of alternative loans that require payments more than once a year, or rates of return on investments that pay interest more than once a year