Answer to Question #244413 in Financial Math for Katie

Question

Jennifer bought j shares of Keester's Koverups for n dollars last year. Her stock rose in price and would eventually earn her 120% capital gain. She decided to sell half of her shares. Represent the capital gain on all of the shares that Jennifer sold algebraically.

a. 0.6jn b. 1.2jn c. 0.5j d. 1.2n

Jennifer bought j shares of Keester's Koverups for n dollars last year. Her stock rose in price and eventually would earn her 120% capital gain. She decided to sell half of her shares. Represent the total value of the shares that were sold algebraically.

a. 1.2jn b. 0.5jn c. 0.6jn d. 1.1jn

Answer 1

1. Let Jennifer bought (j) shares of Keester's for (n) dollars. 

Half of these shares ($\frac{j}{2}$ ) cost in present = $\frac{n}{2}$ dollars .

Now , her stocks appreciate by 120%

So , 

Appreciated Price of (j) stocks = $(1 + 120\%) n$

$= 2.2 n$

Price she gets for selling half the shares $\frac{j}{2} = \frac{2.2n}{2} = 1.1n$

 

Capital Gains for selling half the shares

$=\frac{Value\space of\space half \space stocks\space after\space appreciation - Value\space of\space Half\space stocks\space initially}{Value \space of\space Half\space stocks\space initially}$

$=\frac{1.1n - 0.5n}{0.5n}\\ = 1.2n$

2. Let Jennifer bought (j) shares of Keester's for (n) dollars. 

Half of these shares ($\frac{j}{2}$ ) cost in present = $\frac{n}{2}$ dollars .

Now , her stocks appreciate by 120%

So , 

Appreciated Price of (j) stocks = $(1 + 120\%) n$

$= 2.2 n$

Price she gets for selling half the shares $\frac{j}{2} = \frac{2.2n}{2} = 1.1n$