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1. Comparing Rates :
The Effect of Compounding
Min Vatcharavee 102183026

2. ∗ Quoted Rate / m = stated interest rate
∗ m = the number of times the interest is compounded per year.
Effective interest rate formulas

3. ∗Stated interest rate : The interest rate expressed in terms
of the interest payment made each period .
e.g., 10% annual rate of return on an investment
∗Effective annual interest rate (EAR) : The interest rate expressed as
if were compounded once per year.
e.g., 10.25% annual rate of return on the same investment
WHAT IS EFFECTIVE ANNUAL RATES
AND COMPOUNDING
∗ EAR Actual rate

4. Which bank is better?
Bank A
15 % compounded daily
Bank C
16 % compounded annually
 Bank B
15.5 % compounded quarterly
= 16.18 %
= 16.42%
= 16 %
BANK C BORROWER
BANK B SAVER

5. ∗ A Bank is offering 12 % compounded quarterly
∗ If put $100 in an account ,how much will you
have at the end of one year ? FV
∗ What is the EAR ?
∗ How much will you have at the end of 2 years?
EXAMPLE

6. The bank is effectively offering 12% / 4 = 3 % every quarter

7. Annual percentage rate <APR>
∗ APR is the interest rate charged per period
multiplied by the number of periods per year.
∗ In fact APR is a stated interest rate

8. Example
∗ AmeriCash Advance allows you to write a check
for$120 dated 15 days in the future
∗ They give you $100 today
∗ What are the APR and EAR ?

9. Find the interest rate first, Use Fv formula
FV = pv ( 𝟏+𝟏 ) 𝟏
120 = 100 ( 𝟏+𝟏 )
r = 20 %=0.20
APR = 0.20 x 365/15 = 4.8667 or 486.67%

10. LOAN
Carrine Kezia Aulia
102183022

11. ∗ PURE DISCOUNT LOAN
LOAN TYPES
BORROW REPAY
The borrower receives money today and repays a SINGLE sum
at some time in the future.
SHORT-TERM Loan

12. ∗ A borrower promises to repay $10,000 in 12 months, and the
market interest rate is 7%, how much will the bill sell for in the
market?
EXAMPLE
PV ??
PV= FV
1
1+r
t
FV = $10,000
r = 7% = 0.07
t = 12 months = 1 year
PV = $9,345.79

13. ∗ A borrower promises to repay $15,000 in 36 months, and the
market interest rate is 7%, how much will the bill sell for in the
market?
EXAMPLE
PV ??
PV= FV
1
1+r
t
FV = $15,000
r = 7% = 0.07
t =36 months = 3 year
PV = $12,244.46

14. ∗ INTEREST-ONLY LOANS
LOAN TYPES
Pay interest each period and to repay the entire principal (the original loan amount)
at some point in the future.
BORROW PRINCIPAL
INTEREST
ONLY
INTEREST
ONLY
INTEREST
ONLY

15. ∗ With a three year, 10%, interest-only loan of $1,000, how much
the borrower must pay each year?
EXAMPLE
PRINCIPAL
INTEREST
ONLY
INTEREST
ONLY
INTEREST
ONLY
1st
2nd
3rd
INTEREST ONLY
= $1,000 X 0.10
= $100
$100 $100 $100
$1000

16. ∗ With a four year, 20%, interest-only loan of $2,000, how much the
borrower must pay each year?
EXAMPLE
PRINCIPAL
INTEREST
ONLY
INTEREST
ONLY
INTEREST
ONLY
1st
2nd
3rd
INTEREST ONLY
= $2,000 X 0.20
= $400
$400 $400 $400
$2000
4th
INTEREST
ONLY
$400

17. ∗ AMORTIZED LOANS
LOAN TYPES
Prodiving for a loan to be paid off by making regular principal reductions.
1 2Interest
+
Fixed Amount
Equal amount
Each payment

18. ∗ A business takes out a $5,000, five year loan at 9%. The loan agreement
calls for the borrower to pay the interest on the loan balance each year
and to reduce the load balance each year by $1,000. Calculate the total
payment in each of the remaining years.
1ST
INTEREST PAID = $5,000 X .09

20. ∗ Suppose our five-year, 9%, $5,000 loan was amortized. How would
the amortization schedule look?
2 Equal amount
Each payment
PMT/C ?
PV=
C
( 1+r )t
PV = $5,000
r = 9% = 0.09
t = 5 years
C = $1,285.46

22. ∗ PARTIAL AMORTIZATION
LOAN TYPES
A loan with periodic payments of interest and principal,
but for a shorter term than necessary to pay the principal balance in full
at that rate.
Partially amortizing loans have a balloon payment at some point,
requiring repayment in full or through refinancing.
1st
2nd
3rd
4th
5th

23. ∗ Suppose we have $100,000 loan with a 12% APR and a 20-year
amortization. After 5 years, we win lottery and we can pay off all of our
loan. What will the monthly payment? How big will the balloon payment?
PMT/C ?
PV=
C
( 1+r )t
PV = $100,000
r = 12% = 0.12 yearly = 0.01 monthly
t = 20 years = 240 months
C = $1,101.08

24. ∗ Suppose we have $100,000 loan with a 12% APR and a 20-year
amortization. After 5 years, we win lottery and we can pay off all of our
loan. What will the monthly payment? How big will the balloon payment?
We already pay monthly for 5 years/ 60 months.
The rest we have to pay :
= 240 – 60
= 180 months
PV ? PV=
C
( 1+r )t
pmt = $100,000
r = 12% = 0.12 yearly = 0.01 monthly
t = 15 years = 180 months
PV = $91,743.81

25. ∗ Suppose we have $100,000 loan with a 12% APR and a 20-year
amortization. After 5 years, we win lottery and we can pay off all of our
loan. What will the monthly payment? How big will the balloon payment?
$1,101.08
Per month
$1,101.08
Per month
$1,101.08
Per month
$1,101.08
Per month
$1,101.08
Per month
$91,743.81
Balloon Payment

26. THANK YOU