A bank offers a 2% annual interest rate, compounded annually, for a certain fund. Give an exponential model for a sum of P10,000 invested under this scheme. How much money will there be in the account after 20 years?

The exponential model for an investment with compound interest can be represented by the formula:

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

Where:
- \( A \) is the amount of money after time \( t \),
- \( P \) is the initial investment (principal),
- \( r \) is the annual interest rate (in decimal form),
- \( n \) is the number of times the interest is compounded per year,
- \( t \) is the number of years.

For this problem:
- \( P = 10,000 \),
- \( r = 0.02 \) (2% annual interest),
- \( n = 1 \) (since the interest is compounded annually),
- \( t = 20 \) years.

Using these values, the formula becomes:

\[
A = 10,000 \left(1 + \frac{0.02}{1}\right)^{1 \times 20} = 10,000 \times (1.02)^{20}
\]

Now, let’s calculate the final amount \( A \).After 20 years, the amount of money in the account will be approximately **₱14,859.47**.

Would you like further details or have any questions?

Here are 5 related questions to explore:
1. How would the model change if the interest was compounded quarterly instead of annually?
2. What would be the balance after 30 years instead of 20 years?
3. How much interest would you earn in 20 years if the rate was 3% instead of 2%?
4. What is the doubling time for this investment under the 2% annual interest rate?
5. How much more would you earn if you invested ₱15,000 instead of ₱10,000?

**Tip**: The higher the compounding frequency (e.g., monthly or quarterly), the greater the final balance due to more frequent interest calculations!

Explore how to calculate the amount of money in an account after 20 years for an investment of ₱10,000 at a 2% annual interest rate, compounded annually. Learn the exponential model used in this calculation and understand key concepts like compound interest and exponential growth. Suitable for Grades 10-12.

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