HADM2222, Prof. Q. Ma, Fall 2009
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5. [Discount Rate] You are looking at an investment that will pay $1900 in 5 years if you invest
$1000 today.
What is the implied rate of interest?
Solution
: FV = 1,900; PV=1,000; T=5; we need r. r= (1900/1000)
1/5
– 1 = 13.69%.
6. [Discount Rate] You have landed a fabulous investment opportunity, which can double your
money in 10 years. How good is it?
Solution
: FV = 2; PV=1; T=10; we need r. r=(2/1)
1/10
– 1 = 7.18%.
7. [Implied Rate] Uncle Sam needs quick cash for an emergency and goes to his best friends
Barack and John. Barack offers him $20 million to pay back $24 million in five years, while John
offers him $20 million to pay back $25 million in six years. Which deal is better for Uncle Sam?
Solution:
Barack: FV=24, PV=20, T=5, we need r. r=(24/20)
1/5
– 1 = 3.71%
John: FV=25, PV=20, T=6, we need r. r=(25/20)
1/6
– 1 = 3.79%
It seems Barack is charging a lower rate of return.
8. [Invest for Next Generation] Suppose you have a 1-year old son and you want to provide
$750,000 in 17 years towards his college education. You currently have $50,000 to invest.
What
interest rate must you earn to have the $750,000 when you need it?
Solution:
PV=50,000; FV=750,000; T=17; we need r. r=(750,000/50,000)
1/17
– 1 = 17.27%.
9. [Number of Periods] You expect to receive $250,000 in two years upon graduation. When you
receive it, you will invest it at 7.9 percent per year and plan to withdraw till it reaches $1 million.
How long will it take?
Solution
: PV=250,000; FV=1,000,000; r=7.9%; we need T. T=ln(1,000,000/250,000)/ln(1+.079)
= 18.23.
It takes 18.23 years after receiving the $250,000 at graduation.