Morgan has an investment worth $130,000 dollars after 20 years.  If his original investment was for $50,000 what must the interest rate have been?

To find the interest rate, we can use the formula for compound interest:

\[
A = P(1 + r)^t
\]

Where:
- $A$ is the final amount ($130,000),
- $P$ is the initial investment ($50,000),
- $r$ is the annual interest rate (which we need to find),
- $t$ is the time in years (20 years).

Substitute the given values into the formula:

\[
130,000 = 50,000(1 + r)^{20}
\]

First, divide both sides by 50,000 to simplify:

\[
\frac{130,000}{50,000} = (1 + r)^{20}
\]

\[
2.6 = (1 + r)^{20}
\]

Now, to solve for $r$, take the 20th root of both sides:

\[
(2.6)^{\frac{1}{20}} = 1 + r
\]

\[
1 + r = 2.6^{\frac{1}{20}}
\]

Now subtract 1 from both sides to isolate $r$:

\[
r = 2.6^{\frac{1}{20}} - 1
\]

Let me calculate that value.The interest rate must have been approximately **4.89%** per year.

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. How does the formula change if interest is compounded monthly instead of annually?
2. What would Morgan’s investment be worth after 30 years with the same interest rate?
3. How does the interest rate change if the investment was $100,000 instead of $50,000?
4. What is the difference between simple interest and compound interest in long-term investments?
5. How does inflation affect the real value of Morgan's investment over 20 years?

**Tip:** When calculating compound interest, the time period for compounding (annual, monthly, etc.) can greatly affect the final outcome.

Learn how to calculate compound interest with Morgan's investment problem where he has $130,000 after 20 years from an initial investment of $50,000. Find out the annual interest rate used in the calculation and understand the formula A = P(1 + r)^t. Suitable for high school students and anyone interested in financial mathematics.

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