If Sittipon deposits $2600 today, there will be $4723.41 in his account after Answer years? Suppose the interest rate is 4% compounded quarterly.

We can solve this using the formula for compound interest, which is:

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

Where:
- $A$ is the amount of money in the account after $t$ years.
- $P$ is the initial deposit (the principal).
- $r$ is the annual interest rate (as a decimal).
- $n$ is the number of times the interest is compounded per year.
- $t$ is the number of years.
- $A = 4723.41$, $P = 2600$, $r = 0.04$, and $n = 4$ (since the interest is compounded quarterly).

We need to find $t$, the number of years.

### Rearrange the formula to solve for $t$:

\[
4723.41 = 2600 \left(1 + \frac{0.04}{4}\right)^{4t}
\]

Simplify:

\[
4723.41 = 2600 \left(1.01\right)^{4t}
\]

Now divide both sides by 2600:

\[
\frac{4723.41}{2600} = 1.01^{4t}
\]

\[
1.816695 = 1.01^{4t}
\]

Take the natural logarithm of both sides:

\[
\ln(1.816695) = \ln(1.01^{4t})
\]

Using the logarithmic identity $\ln(a^b) = b \ln(a)$, we get:

\[
\ln(1.816695) = 4t \ln(1.01)
\]

Now, solve for $t$:

\[
t = \frac{\ln(1.816695)}{4 \ln(1.01)}
\]

Let me calculate this.The number of years required for Sittipon's account to grow to $4723.41, at an interest rate of 4% compounded quarterly, is approximately 15 years.

Would you like more details or have any other questions?

Here are 5 related questions for further exploration:
1. What happens if the interest is compounded monthly instead of quarterly?
2. How much would the account contain after 10 years with the same interest rate?
3. What if Sittipon deposits $3000 instead of $2600, keeping the same conditions?
4. How would the result change if the interest rate were 5% instead of 4%?
5. What is the difference between simple and compound interest?

**Tip:** Compound interest grows faster with more frequent compounding periods (e.g., quarterly vs. annually).

Learn how to calculate the number of years for $2600 to grow to $4723.41 at a 4% interest rate compounded quarterly. This detailed solution explores compound interest formulas, logarithmic functions, and algebraic principles. Suitable for students in Grades 10-12.

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