What amount will be received on a sum of X 1750 in 5/2 yr, if the interest is compounded at the rate of 8% pa ?

Options

A. X 2125
B. X 2122.85
C. X 2100
D. X 2200

Answer

To solve the problem of calculating the amount received on a sum of ₹1750 in 5/2 years at an interest rate of 8% per annum compounded annually, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = ₹1750
- Rate of interest (R) = 8% per annum
- Time (T) = 5/2 years = 2.5 years

### Step 2: Convert the rate of interest into decimal form
To convert the percentage rate into decimal form, we divide by 100:
\[ R = \frac{8}{100} = 0.08 \]

### Step 3: Use the compound interest formula
The formula for compound interest is:
\[ A = P \left(1 + \frac{R}{n}\right)^{nt} \]
Where:
- \( A \) = the amount of money accumulated after n years, including interest.
- \( P \) = principal amount (the initial amount of money).
- \( R \) = annual interest rate (decimal).
- \( n \) = number of times that interest is compounded per year.
- \( t \) = the number of years the money is invested or borrowed.

In this case, since the interest is compounded annually, \( n = 1 \).

### Step 4: Substitute the values into the formula
Since the interest is compounded annually:
\[ A = 1750 \left(1 + \frac{0.08}{1}\right)^{1 \times 2.5} \]
\[ A = 1750 \left(1 + 0.08\right)^{2.5} \]
\[ A = 1750 \left(1.08\right)^{2.5} \]

### Step 5: Calculate \( (1.08)^{2.5} \)
Using a calculator:
\[ (1.08)^{2.5} \approx 1.2041 \]

### Step 6: Calculate the final amount
Now, substitute back to find \( A \):
\[ A = 1750 \times 1.2041 \]
\[ A \approx 2107.18 \]

### Step 7: Round off the amount
The amount received is approximately ₹2107.18.

### Final Answer
The amount received on a sum of ₹1750 in 5/2 years at 8% compounded annually is approximately ₹2107.

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