{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Class 4 Jan 16th Completed

The government promises to buy all the output of the

Info iconThis preview shows pages 8–14. Sign up to view the full content.

View Full Document Right Arrow Icon
The government promises to buy all the output of the machine in four years for $400,000. – The machine is worth 0 at this point. – What is the rate of return of this investment? – Timeline or I PV = $355,000 I FV = $400,000 I n = 4 I r = ? 8 FV n = PV 0 ! (1 + r ) n 400 = 355 ! (1 + r ) 4 400 355 " # $ % ' 1 4 = 1 + r r = 400 355 " # $ % ' 1 4 ( 1 = 3.0286% Or in general: r = FV n PV 0 ! " # $ % 1 n ' 1 = FV n PV 0 n ' 1
Background image of page 8

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Example: Solving for the Number of Periods n I You just met the girl of your dreams. I You currently have $10,000 in your Engagement Ring Fund, which earns 12% per year. I The engagement ring you want costs $20,000. I How long do you have to wait before you can pop the question? – What info do we have? I PV = $10,000 I FV = $20,000 I n = ? I r = 12% FV n = PV 0 ! (1 + r ) n => 20, 000 = 10, 000 *(1 + 0.12) n => 2 = (1.12) n " (1.12) n = 2 => ln(1.12) n = ln(2) => n * ln(1.12) = ln(2) => n = ln(2) ln(1.12) => n = 6.1163 Or in general: n = ln FV n PV 0 ( ) ln(1 + r ) 9
Background image of page 9
Aside: The Rule of 72 again I According to the this rule, it would have taken you years to double your money at an annual rate of interest of 12%. 6 12 72 72 = = r 10
Background image of page 10

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Summary n n r PV FV ) 1 ( * + = n n n n r FV r FV PV + = + = ) 1 ( * ) 1 ( 11 ) 1 ln( ln r PV FV n + = 1 1 = n PV FV r
Background image of page 11
Compounding Frequencies: APRs vs. EARs 12
Background image of page 12

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
13 Compounding Frequencies I So far we assumed (implicitly) that compounding occurred once per period. I What happens if interest is compounded more frequently than once a year? I Example: (Note: this is not how banks state returns) A) Bank A offers an effective annual interest rate of r Yr = 12% B) Bank B offers an effective semi-annual rate of r semi = 6% C) Bank C offers an effective quarterly rate of r Q = 3%
Background image of page 13
Image of page 14
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page8 / 16

The government promises to buy all the output of the...

This preview shows document pages 8 - 14. Sign up to view the full document.

View Full Document Right Arrow Icon bookmark
Ask a homework question - tutors are online