SOLUTION: Four years after paying $3400 for shares in a startup company, you sell the shares for $1900 at a loss. What is the total return in percentage and what was the annual return in pe

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Question 1119614: Four years after paying $3400 for shares in a startup company, you sell the shares for $1900 at a loss. What is the total return in percentage and what was the annual return in percentages?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
you bought the shares for 3400.
you sold them for 1900.

your profit ratio is equal to (s - c) / c

s is the sale price.
c is the cost.

this becomes (1900 - 3400) / 3400 = -.4411764706.

a negative profit is a positive loss.

your loss ratio is therefore .4411764706.

multiply that by 100 and your loss percent = 44.11764706.

that's your total loss percent.

to determine the annual loss percent, your would use the following formula.

f = p * (1 + r) ^ n

f is the future value
p is the present value
r is the interest rate per time period, in this case years.
n is the number of time periods, in this case years.

the formula becomes:

1900 = 3400 * (1 + r) ^ 4

divide both sides of this equaton by 3400 to get:

1900 / 3400 = (1 + r) ^ 4

take the fourth root of both sides of the equqtion to get:

(1900 / 3400) ^ (1/4) = 1 + r

subtract 1 from both sides of this equation to get:

(1900 / 3400) ^ (1/4) - 1 = r

solve for r to get:

r = -.135393152.

that's your profit ratio per year.

your loss ratio per year is .135393152 per year.

your loss percent per year is 13.5393152 percent per year.

youo started with 3400 dollars.

each year you lost 13.5393152 percent of it.

your average yearly balance is therefore shown as follows:

beginning of first year = 3400.
end of first year = 2939.663283
end of second year = 2541.653005
end of third year = 2197.530594
end of fourth year = 1900.

each year you multiply your balance from the previous year by .135393152 and then subtract that number from it to get the balance for that year.

for example:

3400 * .13539352 = 460.3367168.
3400 - 460.3367168 = 2939.663283.

this is the balance at the end of the first year as shown above.

your solution is therefore:

the total percent loss is 44.11764706 percent.
the average percent loss each year is 13.5393152 percent.

round to the required number of decimal places.

for example, if you are required to round to 2 decimal places, then your solution is:

44.12% for total percent loss.
13.54% for average percent loss each year.