To solve this problem, we use the formula for simple interest:

$A = P(1 + rt)$

Where:

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

Step 1: Create equations based on given data

1. After 2 years, the amount becomes 5600: $5600 = P(1 + 2r)$

2. After 5 years, the amount becomes 6500: $6500 = P(1 + 5r)$

Step 2: Solve the equations

From the first equation:

$1 + 2r = \frac{5600}{P}$

From the second equation:

$1 + 5r = \frac{6500}{P}$

Step 3: Eliminate $P$ by dividing the two equations

$\frac{1 + 5r}{1 + 2r} = \frac{6500}{5600}$

Simplify the right-hand side: $\frac{6500}{5600} = \frac{65}{56}$

$\frac{1 + 5r}{1 + 2r} = \frac{65}{56}$

Cross-multiply:

$56(1 + 5r) = 65(1 + 2r)$

Expand: $56 + 280r = 65 + 130r$

Simplify: $150r = 9$

$r = \frac{9}{150} = 0.06$

Thus, the rate of interest is $r = 6\%$.

Step 4: Find the principal $P$

Substitute $r = 0.06$ into the first equation: $5600 = P(1 + 2 \cdot 0.06)$

$5600 = P(1.12)$

$P = \frac{5600}{1.12} = 5000$

Final Answer:

• Principal ($P$) = 5000
• Rate of interest ($r$) = 6%

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Would you like a step-by-step verification or additional insights?

Related Questions:

1. What is the total interest earned after 5 years?
2. How would this change for compound interest at the same rate?
3. What would the rate be if the amounts were swapped between 2 and 5 years?
4. How long would it take for the investment to double at 6% simple interest?
5. Can you derive the general formula for principal and rate from given amounts?

Tip:

Always ensure units for time and rate are consistent when working