jacob invested 740000 in savings bank at rate x% compounded quarterly in jan 2020 if total amount received in march 2021 is 900323 what is x

To determine the interest rate \( x\% \) for Jacob's investment, we can use the formula for compound interest:

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

Where:
- \( A \) is the final amount (900,323),
- \( P \) is the initial principal (740,000),
- \( r \) is the annual interest rate (expressed as a decimal),
- \( n \) is the number of times interest is compounded per year (4, since it is compounded quarterly),
- \( t \) is the time in years (from January 2020 to March 2021 is 1 year and 3 months, or \( 1.25 \) years).

We need to solve for \( r \), the annual interest rate. Let's set up the equation:

\[
900323 = 740000 \left( 1 + \frac{r}{4} \right)^{4 \times 1.25}
\]

Now let's solve for \( r \).The annual interest rate \( x \% \) is approximately 16\%.

Would you like further details on how this was calculated or have any other questions?

Here are five related questions to explore further:
1. How does the frequency of compounding affect the total amount received?
2. What would have been the total amount if the interest was compounded annually instead of quarterly?
3. How would a shorter investment period affect the interest earned?
4. How can the formula for compound interest be adapted for continuous compounding?
5. What if Jacob had invested a different amount, how would the interest rate change?

**Tip:** Always ensure you understand how the time and compounding frequency impact compound interest results!

Jacob invested 740,000 in a savings bank at rate x% compounded quarterly in Jan 2020. If the total amount received in March 2021 is 900,323, what is x?

Learn how to calculate the interest rate for Jacob's 740,000 investment, compounded quarterly, using the compound interest formula. This example demonstrates the use of exponential growth and algebraic manipulation to solve for the interest rate. Suitable for students in Grades 10-12.

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