Unformatted text preview: ample Suppose you want to earn an effective rate of
12% and you are looking at an account that
compounds on a monthly basis. What APR must
they [ APR = 12 (1 + .12)
or 11.39% 1 / 12 − 1 = .1138655152 49 Computing Payments with
APRs Suppose you want to buy a new computer system and
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 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
Compounding Suppose you deposit $50 a month into an
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
Compounding You need $15,000 in 3 years for a new car. If
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? 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
based on continuous compounding
EAR = eq – 1 The e is a special function on the calculator normally
denoted by ex
denoted Example: What is the effective annual rate of
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
value of money calculations?
value 54 Pure Discount Loans – Example
6.12 Treasury bills are excellent examples of pure
discount loans. The principal amount is repaid
at some future date, without any periodic
If a T-bill promises to repay $10,000 in 12
months and the market interest rate is 7
percent, how much will the bill sell for in the
market? PV = 10,000 / 1.07 = 9,345.79
55 Interest-Only Loan - Example Consider a 5-year, interest-only loan with a 7%
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
flows on corporate bonds and we will talk about
them in greater detail later.
them 56 Amortized Loan with Fixed Principal
Payment - Example
Payment Consider a $50,000, 10 year loan at 8%
interest. The loan agreement requi...
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