To calculate how much the businessman would earn in total after 6 years, we can use the formula for compound interest:

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

Where:

• $A$ is the amount of money accumulated after $t$ years, including interest.
• $P$ is the principal amount (Rs. 200,000).
• $r$ is the annual interest rate (5% or 0.05).
• $n$ is the number of times the interest is compounded per year (since it's yearly, $n = 1$).
• $t$ is the number of years (6 years).

Substituting the values into the formula:

$A = 200,000 \left( 1 + \frac{0.05}{1} \right)^{1 \times 6}$ $A = 200,000 \left( 1 + 0.05 \right)^{6}$ $A = 200,000 \left( 1.05 \right)^{6}$ $A = 200,000 \times 1.3401$ $A \approx 268,020$

So, after 6 years, the businessman will have a total amount of Rs. 268,020.

The total earnings (interest earned) are:

$\text{Total Earnings} = A - P = 268,020 - 200,000 = 68,020$

Thus, the businessman would earn Rs. 68,020 in total over 6 years.

Let me know if you need more details!

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Here are 5 related questions:

1. How would the total amount change if the interest were compounded quarterly?
2. What would the total amount be if the interest rate were 6% instead of 5%?
3. How do you calculate the compound interest when the principal is increased every year?
4. What is the difference between simple and compound interest over a period of time?
5. How does the number of compounding periods (annually, quarterly, monthly) affect the total amount?

Tip: The more frequently interest is compounded, the greater the amount will grow over time.