A person bought a motorbike under the following scheme: Down payment of Rs. 15,000 and the rest amount at 8% per annum for 2 years. In this way, he paid Rs. 28,920 in total. Find the actual price of the motorbike.

Options

A. Rs. 26,000
B. Rs. 27,000
C. Rs. 27,200
D. Rs. 26,500

Answer

To find the actual price of the motorbike, we can follow these steps:

### Step 1: Define the variables
Let the actual price of the motorbike be \( x \).

### Step 2: Calculate the remaining amount after the down payment
The down payment made is Rs. 15,000. Therefore, the remaining amount to be financed is:
\[ \text{Remaining Amount} = x - 15,000 \]

### Step 3: Calculate the total amount paid
The total amount paid for the motorbike is Rs. 28,920. This includes the down payment and the amount financed with interest. Thus, we can express this as:
\[ \text{Total Amount} = \text{Down Payment} + \text{Amount Financed with Interest} \]
\[ 28,920 = 15,000 + \text{Amount Financed with Interest} \]
From this, we can find the amount financed with interest:
\[ \text{Amount Financed with Interest} = 28,920 - 15,000 = 13,920 \]

### Step 4: Use the formula for compound interest
The amount financed is subject to an interest rate of 8% per annum for 2 years. The formula for the amount \( A \) in compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
Where:
- \( A \) is the total amount after interest,
- \( P \) is the principal amount (the remaining amount),
- \( r \) is the rate of interest,
- \( n \) is the number of years.

Substituting the known values:
\[ 13,920 = (x - 15,000) \left(1 + \frac{8}{100}\right)^2 \]
\[ 13,920 = (x - 15,000) \left(1.08\right)^2 \]
\[ 13,920 = (x - 15,000) \times 1.1664 \]

### Step 5: Solve for \( x - 15,000 \)
Now, we can isolate \( x - 15,000 \):
\[ x - 15,000 = \frac{13,920}{1.1664} \]
Calculating the right-hand side:
\[ x - 15,000 \approx 11,925.56 \]

### Step 6: Solve for \( x \)
Now, add the down payment back to find \( x \):
\[ x = 11,925.56 + 15,000 \]
\[ x \approx 26,925.56 \]

### Step 7: Round to the nearest whole number
Since prices are typically rounded to the nearest whole number, we can round this to:
\[ x \approx 26,926 \]

### Final Answer
The actual price of the motorbike is approximately Rs. 26,926.

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