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**Unformatted text preview: **ample Suppose you want to earn an effective rate of
Suppose
12% and you are looking at an account that
compounds on a monthly basis. What APR must
they pay?
they [ APR = 12 (1 + .12)
or 11.39% 1 / 12 − 1 = .1138655152 49 Computing Payments with
Computing
APRs
APRs Suppose you want to buy a new computer system and
Suppose
the store is willing to sell it to allow you to make
monthly payments. The entire computer system costs
$3,500. The loan period is for 2 years and the interest
rate is 16.9% with monthly compounding. What is your
monthly payment?
monthly Monthly rate = .169 / 12 = .01408333333
Number of months = 2(12) = 24
3,500 = C[1 – (1 / 1.01408333333)24] / .01408333333
C = 172.88 50 Future Values with Monthly
Future
Compounding
Compounding Suppose you deposit $50 a month into an
Suppose
account that has an APR of 9%, based on
monthly compounding. How much will you have
in the account in 35 years?
in Monthly rate = .09 / 12 = .0075
Number of months = 35(12) = 420
FV = 50[1.0075420 – 1] / .0075 = 147,089.22 51 Present Value with Daily
Present
Compounding
Compounding You need $15,000 in 3 years for a new car. If
You
you can deposit money into an account that
pays an APR of 5.5% based on daily
compounding, how much would you need to
deposit?
deposit? Daily rate = .055 / 365 = .00015068493
Number of days = 3(365) = 1,095
FV = 15,000 / (1.00015068493)1095 = 12,718.56 52 Continuous Compounding Sometimes investments or loans are figured
Sometimes
based on continuous compounding
based
EAR = eq – 1 The e is a special function on the calculator normally
The
denoted by ex
denoted Example: What is the effective annual rate of
Example:
7% compounded continuously?
7% EAR = e.07 – 1 = .0725 or 7.25% 53 Quick Quiz – Part V What is the definition of an APR? What is the effective annual rate? Which rate should you use to compare
Which alternative investments or loans?
alternative Which rate do you need to use in the time
Which
value of money calculations?
value 54 Pure Discount Loans – Example
Pure
6.12
6.12 Treasury bills are excellent examples of pure
Treasury
discount loans. The principal amount is repaid
at some future date, without any periodic
interest payments.
interest
If a T-bill promises to repay $10,000 in 12
If
months and the market interest rate is 7
percent, how much will the bill sell for in the
market?
market? PV = 10,000 / 1.07 = 9,345.79
55 Interest-Only Loan - Example Consider a 5-year, interest-only loan with a 7%
Consider
interest rate. The principal amount is $10,000.
Interest is paid annually.
Interest What would the stream of cash flows be?
• Years 1 – 4: Interest payments of .07(10,000) = 700
• Year 5: Interest + principal = 10,700 This cash flow stream is similar to the cash
This
flows on corporate bonds and we will talk about
them in greater detail later.
them 56 Amortized Loan with Fixed Principal
Amortized
Payment - Example
Payment Consider a $50,000, 10 year loan at 8%
Consider
interest. The loan agreement requi...

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