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The problem asks: In what time will RM2500 amount to RM3500 at 6% p.a. compounded quarterly?

To solve this, we can use the formula for compound interest:

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

Where:
- \(A\) is the final amount (RM3500),
- \(P\) is the initial principal (RM2500),
- \(r\) is the annual interest rate (6% or 0.06),
- \(n\) is the number of times interest is compounded per year (quarterly means \(n = 4\)),
- \(t\) is the time in years (which we are solving for).

Let's solve for \(t\):

\[
3500 = 2500 \left( 1 + \frac{0.06}{4} \right)^{4t}
\]

First, simplify the equation:

\[
3500 = 2500 \left( 1 + 0.015 \right)^{4t}
\]

\[
3500 = 2500 (1.015)^{4t}
\]

Next, divide both sides by 2500:

\[
1.4 = (1.015)^{4t}
\]

Now, take the natural logarithm (ln) of both sides to solve for \(t\):

\[
\ln(1.4) = 4t \cdot \ln(1.015)
\]

Solve for \(t\):

\[
t = \frac{\ln(1.4)}{4 \cdot \ln(1.015)}
\]

Let me calculate this value for you.The time required for RM2500 to amount to RM3500 at a 6% annual interest rate, compounded quarterly, is approximately 5.65 years.

Would you like further details or clarification on any part of this calculation?

Here are 5 related questions to consider:
1. How does the frequency of compounding affect the growth of an investment?
2. What would the time be if the interest were compounded annually instead of quarterly?
3. How much would RM2500 amount to in 10 years at the same interest rate and compounding period?
4. What would the time be if the interest rate were increased to 8% p.a.?
5. How can you calculate the interest earned over a given period?

**Tip:** Always make sure to adjust the compounding periods (e.g., quarterly, annually) in the formula for compound interest calculations!

In what time will RM2500 amount to RM3500 at 6% p.a. compounded quarterly?

Learn how to calculate the time required for RM2500 to amount to RM3500 with an interest rate of 6% p.a. compounded quarterly. This example applies the compound interest formula and uses logarithms to solve for time.

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