At what rate was an investment made that obtains ₱2520 on ₱10500 over four years

To determine the rate at which an investment grows, we use the formula for simple interest:

\[
A = P(1 + rt)
\]

Where:
- \(A\) is the final amount,
- \(P\) is the principal (initial investment),
- \(r\) is the rate of interest per year (in decimal form),
- \(t\) is the time in years.

From the problem, we have:
- \(A = ₱2520 + ₱10500 = ₱13020\),
- \(P = ₱10500\),
- \(t = 4 \, \text{years}\).

Now, substituting the known values into the formula:

\[
₱13020 = ₱10500(1 + r \times 4)
\]

Let's solve for \(r\):

\[
13020 = 10500(1 + 4r)
\]

Dividing both sides by 10500:

\[
\frac{13020}{10500} = 1 + 4r
\]

\[
1.24 = 1 + 4r
\]

Subtracting 1 from both sides:

\[
0.24 = 4r
\]

Finally, dividing both sides by 4:

\[
r = \frac{0.24}{4} = 0.06
\]

Thus, the rate of interest is **6% per year**.

Would you like more details or have any questions?

Here are some related questions to explore:
1. What is the formula for compound interest?
2. How would the result change if the interest were compounded annually?
3. How does the principal amount affect the final amount?
4. What would be the total amount after 6 years at the same rate?
5. What if the interest was paid monthly instead of annually?

**Tip:** When dealing with interest calculations, ensure you're clear on whether it's simple or compound interest. This affects the outcome significantly!

At what rate was an investment made that obtains ₱2520 on ₱10500 over four years?

Learn how to calculate the rate of an investment that earns ₱2520 on an initial investment of ₱10500 over four years using the simple interest formula. This problem covers algebraic concepts and interest rate calculations, suitable for students in Grades 9-12.

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