Annuity Basics
A series of equal, periodic cash flows for a specified period of time is called this.
What is an Annuity?
Explanation: An annuity consists of equal payments made at regular intervals for a set number of periods. Car loans and mortgages are common examples.
On the financial calculator, this button represents the equal payment in an annuity.
What is PMT?
Explanation: PMT is the periodic annuity payment.
For example, receiving $1,000 every year means PMT = $1,000
Rent paid at the beginning of every month is an example of this type of annuity.
What is an Annuity Due?
Explanation: The important phrase is beginning of the month. Beginning-of-period payments mean annuity due.
If payments are not equal from period to period, they are called this type of cash flow.
What are Uneven Cash Flows?
Explanation: An example would be:
Year 1 = $100
Year 2 = $150
Year 3 = $300
Because the amounts are different, they are not an annuity.
This is the annual interest rate that is normally quoted or advertised.
What is APR?
Explanation: APR stands for Annual Percentage Rate. The chapter describes it as the annual rate quoted under lending rules.
In this type of annuity, payments occur at the end of each period.
What is an Ordinary Annuity?
Explanation: An ordinary annuity has payments at the end of each period. A car loan is one example.
Finding what a series of future annuity payments is worth today means solving for this.
What is Present Value?
Explanation: Present Value asks what all of those future payments are worth today.
The chapter gives the ordinary-annuity PV formula:
PV = PMT × [1 − 1/(1 + r)ⁿ] ÷ r
To solve an annuity due on a financial calculator, you should switch the calculator into this mode.
What is Begin Mode?
Explanation: The calculator must recognize that the cash flows occur at the beginning rather than the end.
2nd → BGN → 2nd → SET
And importantly, switch it back afterward.
This type of loan has one lump-sum repayment at the end and no periodic interest payments.
What is a Pure Discount Loan?
Explanation: The borrower receives money today and makes one future payment. Ex) Treasury bills.
This interest rate reflects the actual annual return or cost after accounting for compounding.
What is EAR?
Explanation: EAR stands for Effective Annual Rate.
Unlike APR, EAR incorporates the effect of compounding.
In this type of annuity, payments occur at the beginning of each period.
What is an Annuity Due?
Explanation: An annuity due has payments at the beginning of each period. Rent or lease payments are common examples.
Finding what a series of deposits will grow to at the end of the investment period means solving for this.
What is Future Value?
Explanation: Future Value tells us what repeated deposits will accumulate to after earning interest.
The formula is:
FV = PMT × [(1 + r)ⁿ − 1] ÷ r
A stream of equal cash flows that continues forever is called this.
What is a Perpetuity?
Explanation: Unlike an annuity, a perpetuity has no ending date.
This type of loan requires periodic interest payments, while the full principal is repaid at the end.
What is an Interest-Only Loan?
Explanation: With an interest-only loan, principal does not gradually decrease.
The borrower pays interest throughout the loan and then repays the principal at maturity. Many corporate bonds have this structure.
A 12% APR compounded monthly has this monthly periodic interest rate.
What is 1%?
Explanation:
Period Rate = APR ÷ Number of Periods
12% ÷ 12 = 1% per month
The chapter specifically warns that APR can be divided by the number of periods to obtain the periodic rate, but EAR should not be divided this way.
Unless a problem tells you otherwise, Chapter 5 assumes that cash flows occur at this point during each period.
What is the end of the period?
Explanation: If the problem does not specifically say payments occur at the beginning, assume an ordinary annuity, meaning end-of-period payments.
You deposit $100 at the end of each year for 3 years at 10%. The Future Value of this ordinary annuity is this amount.
What is $331?
Explanation:
The deposits grow differently because they are made at different times:
Year 1 deposit grows for 2 years:
$100(1.10)² = $121
Year 2 deposit grows for 1 year:
$100(1.10) = $110
Year 3 deposit:
$100
Add them:
$121 + $110 + $100 = $331
The Present Value of a perpetuity is calculated by dividing its cash flow by this.
What is the Interest Rate?
Explanation:
The perpetuity formula is:
PV = C ÷ r
where:
C = periodic cash flow
r = discount rate
A typical car loan, where each payment includes both interest and some repayment of principal, is this type of loan.
What is an Amortized Loan?
Explanation: An amortized loan gradually reduces the principal. Each payment includes:
Interest + Principal repayment
Most consumer loans and mortgages use this structure.
A 12% APR compounded monthly has an Effective Annual Rate of approximately this.
What is 12.68%?
Explanation:
The formula is:
EAR = (1 + APR/m)^m − 1
So:
EAR = (1 + .12/12)¹² − 1
EAR ≈ 12.68%
When a problem contains several cash flows occurring at different times, drawing this can help organize when each cash flow occurs.
What is a Timeline?
Explanation: Timelines help students track when cash flows occur. Time 0 represents today, while later tick marks represent future periods.
You borrow $100,000 and repay it with five equal annual payments at 18%. The annual payment is approximately this amount.
What is $31,977.78?
Explanation: On the financial calculator:
PV = 100,000
I/Y = 18
N = 5
CPT → PMT
PMT = -$31,977.78
A perpetuity pays $100 every year forever. If the discount rate is 5%, its Present Value is this.
What is $2,000?
Explanation:
PV = C ÷ r
PV = $100 ÷ .05
PV = $2,000
A $10,000 interest-only loan has a 7% annual rate. The annual interest payment is this amount.
What is $700?
Explanation:
Interest payment:
$10,000 × .07 = $700
For the example in the chapter:
Years 1 through 4 = $700
Year 5 = $700 interest + $10,000 principal = $10,700
One savings account pays 5.25% APR compounded daily and another pays 5.30% APR compounded semiannually. According to the Chapter 5 example, this account has the higher EAR.
What is the 5.25% account compounded daily?
Explanation: Although its stated APR is lower, the more frequent compounding produces the slightly higher effective rate:
5.25% daily → EAR ≈ 5.39%
5.30% semiannual → EAR ≈ 5.37%