To solve this, we need to determine the principal ($P$) and the rate of interest ($r$) under simple interest.

Formula for Simple Interest

The total amount ($A$) in simple interest is given by: $A = P(1 + rt)$ where:

• $A$ is the total amount after $t$ years.
• $P$ is the principal.
• $r$ is the annual rate of interest (in decimal form).
• $t$ is the time in years.

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Given Data:

1. After 2 years, the amount is $A_1 = 5600$. $5600 = P(1 + 2r)$ (Equation 1)

2. After 5 years, the amount is $A_2 = 6500$. $6500 = P(1 + 5r)$ (Equation 2)

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Solving for $P$ and $r$:

Step 1: Solve Equation 1 for $P$

From Equation 1: $P = \frac{5600}{1 + 2r}$ (Substitute $P$ into Equation 2)

Step 2: Substitute into Equation 2

Using Equation 2: $6500 = \frac{5600}{1 + 2r}(1 + 5r)$ Simplify: $6500(1 + 2r) = 5600(1 + 5r)$ $6500 + 13000r = 5600 + 28000r$ $13000r - 28000r = 5600 - 6500$ $-15000r = -900$ $r = \frac{900}{15000} = 0.06$ So, the rate of interest ($r$) is 6% per year.

Step 3: Solve for $P$

Substitute $r = 0.06$ into Equation 1: $P = \frac{5600}{1 + 2(0.06)}$ $P = \frac{5600}{1.12} = 5000$

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Final Answer:

1. The principal is $P = 5000$.
2. The rate of interest is $r = 6\%$ per year.

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Would you like further clarification on this or details about the calculation?
Here are some related questions to explore:

1. How does compound interest differ from simple interest?
2. Can we calculate the total interest earned in these 2 and 5 years?
3. What would the amount be if the rate of interest was 7% instead?
4. How can the formula for simple interest be derived?
5. What are real-life applications of simple interest in financial decisions?

Tip: Always ensure the time period for the rate of interest matches