https://file.aiquickdraw.com/mathbot/file/1727056064420dqa0fb7q.jpg

The text from the image is in Indonesian and translates to:

"With compound interest, a sum of money invested for 5 years will increase by 20% from the initial amount. If the interest calculation is done monthly, the annual interest rate from this investment is ..."

This problem involves compound interest, and we need to find the annual interest rate when the total growth after 5 years (compounded monthly) results in a 20% increase. 

The formula for compound interest is:

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

Where:
- \( A \) is the final amount (120% or 1.20 of the initial principal \( P \)),
- \( P \) is the principal (initial investment),
- \( r \) is the annual interest rate,
- \( n \) is the number of times the interest is compounded per year (12 for monthly),
- \( t \) is the time in years (5 years).

We are given:
- \( A = 1.20P \),
- \( t = 5 \),
- \( n = 12 \).

We will solve for \( r \). Let me calculate the value.The equation for the compound interest, when solved algebraically, turns out to be highly complex. Instead of manually solving it symbolically, I will compute the approximate solution numerically to find the annual interest rate \( r \). Let me do that now.The annual interest rate for this investment, compounded monthly, is approximately **3.65%**.

Would you like more details or have any further questions?

Here are 5 related questions you might find interesting:
1. How does the frequency of compounding affect the final amount?
2. What is the difference between simple interest and compound interest?
3. How would the interest rate change if compounding was done quarterly instead of monthly?
4. How can I calculate the interest rate if I know the final amount, principal, and time period?
5. What happens if the investment duration changes to 10 years with the same interest rate?

**Tip:** When working with compound interest, increasing the frequency of compounding (monthly, weekly, etc.) will generally increase the final amount, but the difference becomes smaller as the frequency increases.

Dengan suku bunga majemuk, sejumlah uang yang diinvestasikan selama 5 tahun akan bertambah 20% dari sebelumnya. Jika perhitungan bunga dilakukan setiap bulan, besar suku bunga per tahun dari investasi tersebut adalah ...

Learn how to calculate the annual interest rate for a compound interest investment, where a 5-year investment grows by 20% with monthly interest compounding. This problem explores exponential growth and compound interest formulas, suitable for Grades 10-12.

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