Solving for Rates What annual rate of return is earned on a $2,000 investment made in year 3 when it grows to $3,000 by the end of year six?
A) 6.99%
B) 14.47%
C) 24.00%
D) 50.00%

Question

Quizplus · Accepted Answer

To solve for the annual rate of return, we can use the following formula:

Ending value = Beginning value x (1 + rate)^n

where:
- Ending value = $3,000
- Beginning value = $2,000
- n = 3 years

Plugging in the values and solving for the rate, we get:

$3,000 = $2,000 x (1 + rate)^3
1.5 = (1 + rate)^3
log(1.5) = log(1 + rate)^3
log(1.5) = 3 log(1 + rate)
log(1 + rate) = log(1.5) / 3
1 + rate = e^(log(1.5) / 3)
rate = e^(log(1.5) / 3) - 1
rate = 14.47%

Therefore, the best choice is B, which corresponds to a rate of 14.47%.

Solving for Rates What Annual Rate of Return Is Earned