At a simple interest 800 becomes 956 in three years. If the interest rate, is increased by 3%, how much would ` 800 become in three years?

Options

A. A) 1020.8
B. B) 1004
C. C) 1028
D. D) Data inadequate

Answer

To solve the problem step by step, we need to find out how much `800 will become in three years if the interest rate is increased by 3%.

### Step 1: Determine the original interest rate
We know:
- Principal (P) = 800
- Amount (A) = 956
- Time (T) = 3 years

Using the formula for Simple Interest (SI):
\[ SI = A - P \]
So,
\[ SI = 956 - 800 = 156 \]

Now, we can use the formula for Simple Interest:
\[ SI = \frac{P \times R \times T}{100} \]
Substituting the known values:
\[ 156 = \frac{800 \times R \times 3}{100} \]

### Step 2: Solve for R (the original rate)
Rearranging the equation gives:
\[ 156 = \frac{2400R}{100} \]
Multiplying both sides by 100:
\[ 15600 = 2400R \]
Now, dividing both sides by 2400:
\[ R = \frac{15600}{2400} \]
Calculating this gives:
\[ R = 6.5\% \]

### Step 3: Determine the new interest rate
The problem states that the interest rate is increased by 3%. Therefore, the new rate (R') is:
\[ R' = 6.5 + 3 = 9.5\% \]

### Step 4: Calculate the new amount after 3 years with the new interest rate
Using the formula for Simple Interest again with the new rate:
\[ SI' = \frac{P \times R' \times T}{100} \]
Substituting the known values:
\[ SI' = \frac{800 \times 9.5 \times 3}{100} \]

### Step 5: Calculate SI'
Calculating the above expression:
\[ SI' = \frac{800 \times 9.5 \times 3}{100} = \frac{22800}{100} = 228 \]

### Step 6: Calculate the new amount
Now, we find the new amount (A'):
\[ A' = P + SI' \]
Substituting the values:
\[ A' = 800 + 228 = 1028 \]

Thus, the amount `800 will become in three years at the new interest rate is **1028**.

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