Question
Question

What rate of interest compounded annually is required to double an investment in 3 years?

 

Round your percentage to 2 decimal points.
Provide your answer below:
%  (Round your percentage to $2$  decimal places. Do not enter a percent sign.)

To find the rate of interest compounded annually that is required to double an investment in 3 years, we can use the formula for compound interest:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $ A $ is the final amount,
- $ P $ is the principal amount (initial investment),
- $ r $ is the annual interest rate (as a decimal),
- $ n $ is the number of times the interest is compounded per year (since it's compounded annually, $ n = 1 $),
- $ t $ is the number of years.

In this case, we want the final amount $ A $ to be twice the principal $ P $, so $ A = 2P $, and the time $ t $ is 3 years. We are solving for $ r $.

Starting with the compound interest formula and substituting values:

\[
2P = P \left(1 + r\right)^3
\]

Dividing both sides by $ P $:

\[
2 = (1 + r)^3
\]

Now, take the cube root of both sides:

\[
\sqrt[3]{2} = 1 + r
\]

Subtract 1 from both sides:

\[
r = \sqrt[3]{2} - 1
\]

Now let's calculate the value of $ r $.The required annual interest rate to double an investment in 3 years, compounded annually, is approximately **25.99%**.

Would you like more details on this calculation or have any further questions?

Here are 5 related questions:
1. How would the interest rate change if the investment period was 5 years instead of 3?
2. How does the interest rate change if the interest is compounded quarterly instead of annually?
3. What is the formula for continuous compound interest?
4. What is the effective annual rate (EAR) if the interest is compounded more frequently than annually?
5. Can this method be applied to investments that increase by more than double in a given period?

**Tip:** The rule of 72 provides a quick way to estimate how long it takes for an investment to double with compound interest! Just divide 72 by the annual interest rate to get the approximate time in years.

What rate of interest compounded annually is required to double an investment in 3 years? (Round your percentage to 2 decimal points.)

Find out the annual interest rate required to double an investment in 3 years using compound interest. This detailed solution walks through the formula, relevant algebra, and calculations, providing an interest rate rounded to 2 decimal points. Ideal for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation