SOLUTION: an investor bought a stock for 18,000. five years later, the stock was sold for 22,000. if interest is compounded continuously, what annual nominal rate of interest did the origina

Question 1135489: an investor bought a stock for 18,000. five years later, the stock was sold for 22,000. if interest is compounded continuously, what annual nominal rate of interest did the original 18,000 investment earn? Give answer as a percentage and round your answer to 2 decimal places.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the continuous compounding formula is f = p * e^(r * n)

f is the future value.
p is the present value
r is the interest rate per time period.
n is the number of time periods.

in your problem:

f = 22000
p = 18000
n = 5
r = what you want to find.

the formula becomes 22000 = 18000 * e^(5r)

divide both sides of the equation by 18000 to get 22000 / 18000 = e^(5r)

take the natural log of both sides of this equaiton to get ln(22000 / 18000) = ln(e^(5r)).

since ln(e^(5r) is equal to 5r * ln(e) and since ln(e) is equal to 1, then ln(e^5r)) becomes 5r.

your equaation becomes ln(22000/18000) = 5r

solve for r to get r = ln(22000/18000) / 5 = .0401341391.

that's your continuous compounding rate per year.

confirm by evaluating the original equation to get 22000 = 18000 * e^(.0401341391 * 5) which results in 22000 = 22000

your solution is that the continuous compounding interest rate per year is equal to 4.01% when expressed as a percent rounded to 2 decimal digits.

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