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**Unformatted text preview: **an solve for the fourth If you are using a financial calculator, be sure
If
and remember the sign convention or you will
receive an error (or a nonsense answer) when
solving for r or t
solving
20 Discount Rate Often we will want to know what the implied
Often
interest rate is in an investment
interest
Rearrange the basic PV equation and solve for r FV = PV(1 + r)t
r = (FV / PV)1/t – 1 If you are using formulas, you will want to make
If
use of both the yx and the 1/x keys
use 21 Discount Rate – Example 1 You are looking at an investment that will pay
You
$1,200 in 5 years if you invest $1,000 today.
What is the implied rate of interest?
What r = (1,200 / 1,000)1/5 – 1 = .03714 = 3.714%
Calculator – the sign convention matters!!!
•
•
•
• N=5
PV = -1,000 (you pay 1,000 today)
FV = 1,200 (you receive 1,200 in 5 years)
CPT I/Y = 3.714% 22 Discount Rate – Example 2 Suppose you are offered an investment
Suppose that will allow you to double your money in
6 years. You have $10,000 to invest.
What is the implied rate of interest?
What r = (20,000 / 10,000)1/6 – 1 = .122462 =
12.25%
12.25% 23 Discount Rate – Example 3 Suppose you have a 1-year old son and
Suppose you want to provide $75,000 in 17 years
towards his college education. You
currently have $5,000 to invest. What
interest rate must you earn to have the
$75,000 when you need it?
$75,000 r = (75,000 / 5,000)1/17 – 1 = .172688 =
17.27%
17.27% 24 Quick Quiz – Part III What are some situations in which you might want to
What
know the implied interest rate?
know
You are offered the following investments: You can invest $500 today and receive $600 in 5 years. The
You
investment is considered low risk.
investment
You can invest the $500 in a bank account paying 4%.
What is the implied interest rate for the first choice and which
What
investment should you choose?
investment 25 Finding the Number of Periods Start with basic equation and solve for t
Start (remember your logs)
(remember FV = PV(1 + r)t
t = ln(FV / PV) / ln(1 + r) You can use the financial keys on the
You calculator as well; just remember the sign
convention.
convention. 26 Number of Periods – Example 1 You want to purchase a new car and you
You are willing to pay $20,000. If you can
invest at 10% per year and you currently
have $15,000, how long will it be before
you have enough money to pay cash for
the car?
the t = ln(20,000 / 15,000) / ln(1.1) = 3.02 years 27 Number of Periods – Example 2 Suppose you want to buy a new house. You
Suppose
currently have $15,000 and you figure you
need to have a 10% down payment plus an
additional 5% of the loan amount for closing
costs. Assume the type of house you want will
cost about $150,000 and you can earn 7.5%
per year, how long will it be before you have
enough money for the down payment and
closing costs?
closing 28 Number of Periods – Example 2
Number
Continued
Continued How much do you need to have in the future? Down payment = .1(150,000) = 15,000 Closing costs = .05...

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