Riya saves an amount of 500 every year and then lent that amount at an interest of 10 precent compounded annually. Find the amount after 3 years.

Options

A. 1820.5
B. 1840.35
C. 1920.5
D. 1940.5

Explanation

To find the total amount Riya will have after saving and lending 500 every year at a compound interest rate of 10% for 3 years, we can follow these steps:

### Step 1: Understand the Problem
Riya saves 500 every year and lends it at a compound interest rate of 10% per annum. We need to calculate the total amount after 3 years.

### Step 2: Calculate the Amount for Each Year
We will calculate the amount for each year separately since Riya saves the amount annually.

#### Amount after Year 1:
- Principal (P) = 500
- Rate (R) = 10%
- Time (n) = 1 year

Using the formula for compound amount:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]
\[ A_1 = 500 \left(1 + \frac{10}{100}\right)^1 \]
\[ A_1 = 500 \left(1 + 0.10\right)^1 \]
\[ A_1 = 500 \times 1.1 \]
\[ A_1 = 550 \]

#### Amount after Year 2:
For the second year, the amount from the first year will also earn interest.
- Principal (P) = 500 (new amount saved)
- Total amount from Year 1 = 550
- Time (n) = 2 years

\[ A_2 = 500 \left(1 + \frac{10}{100}\right)^2 \]
\[ A_2 = 500 \left(1.1\right)^2 \]
\[ A_2 = 500 \times 1.21 \]
\[ A_2 = 605 \]

#### Amount after Year 3:
For the third year, the amounts from the previous years will also earn interest.
- Principal (P) = 500 (new amount saved)
- Total amount from Year 2 = 605
- Time (n) = 3 years

\[ A_3 = 500 \left(1 + \frac{10}{100}\right)^3 \]
\[ A_3 = 500 \left(1.1\right)^3 \]
\[ A_3 = 500 \times 1.331 \]
\[ A_3 = 665.5 \]

### Step 3: Calculate Total Amount After 3 Years
Now, we will add the amounts from all three years to find the total amount Riya will have.

Total Amount = Amount after Year 1 + Amount after Year 2 + Amount after Year 3
\[ \text{Total Amount} = 550 + 605 + 665.5 \]
\[ \text{Total Amount} = 1820.5 \]

### Final Answer
The total amount Riya will have after 3 years is **1820.5 rupees**.

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