7500 becomes 9000 in 3 Years at certain rate of interest. If the rate of interest is decreased by 1% then find the amount?

Options

A. Rs 8600
B. Rs 8525
C. Rs 8775
D. Rs 8500

Answer

To solve the problem step by step, we will follow the process of calculating the simple interest and then adjusting for the decrease in the rate of interest.

### Step 1: Identify the given values
- Principal (P) = 7500
- Amount (A) = 9000
- Time (T) = 3 years

### Step 2: Calculate the Simple Interest (SI)
The formula for Simple Interest is:
\[ \text{SI} = \text{A} - \text{P} \]

Substituting the values:
\[ \text{SI} = 9000 - 7500 = 1500 \]

### Step 3: Calculate the Rate of Interest (R)
Using the formula for Simple Interest:
\[ \text{SI} = \frac{P \times R \times T}{100} \]

Rearranging to find R:
\[ R = \frac{\text{SI} \times 100}{P \times T} \]

Substituting the known values:
\[ R = \frac{1500 \times 100}{7500 \times 3} \]
\[ R = \frac{150000}{22500} = 6.67\% \]

### Step 4: Decrease the Rate of Interest by 1%
New Rate (R') = R - 1
\[ R' = 6.67 - 1 = 5.67\% \]

### Step 5: Calculate the new amount with the decreased rate
Using the formula for the new Simple Interest with the new rate:
\[ \text{SI'} = \frac{P \times R' \times T}{100} \]

Substituting the values:
\[ \text{SI'} = \frac{7500 \times 5.67 \times 3}{100} \]
\[ \text{SI'} = \frac{127575}{100} = 1275.75 \]

### Step 6: Calculate the new amount (A')
New Amount (A') = Principal + New Simple Interest
\[ A' = 7500 + 1275.75 = 8775.75 \]

Since we generally round to the nearest whole number in financial calculations, we can round this to:
\[ A' = 8776 \]

### Final Answer
The new amount after decreasing the rate of interest by 1% is approximately **8776**.

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