Question

At a certain rate of compound interest, 1 grows to 3. What is the rate of interest?

1) 100%
2) 200%
3) 300%
4) 400%

Answer 1

The rate of interest is 200%. Option B is answer.

Step-by-step explanation:

Let x be the rate of interest. We can set up the following equation to represent the compound interest:

3 = 1 * (1 + x/100)^n

where n is the number of compounding periods.

Since the interest rate is unknown, we can set up a system of equations by assuming two different values for n. Let's assume n = 1 and n = 2:

n = 1:

3 = 1 * (1 + x/100)^1

3 = 1 + x/100

x/100 = 2

x = 200%

n = 2:

3 = 1 * (1 + x/100)^2

3 = 1 + 2x/100 + x^2/10000

Simplifying this equation and solving for x leads to the same answer: x = 200%

Therefore, regardless of the number of compounding periods, the rate of interest needed to achieve a final value of 3 is 200%.

Option B is answer.