Question

calculate the amount and the compound interest on \\( \text{rs. } 4600 \\) in \\( 2 \\) years when the rates of interest of successive years are \\( 10\\% \\) and \\( 12\\% \\) respectively.

meenal lends \\( \text{rs. } 75000 \\) at c.i. for \\( 3 \\) years. if the rate of interest for the first two years is \\( 15\\% \\) per year and for the third year it is \\( 16\\% \\), calculate the sum meenal will get at the end of third year.

calculate the compound interest for the second year on \\( \text{rs. } 8000 \\) invested for \\( 3 \\) years at \\( 10\\% \\) per annum.

a man invested \\( \text{rs. } 46875 \\) at \\( 4\\% \\) per annum compound interest for \\( 3 \\) years. calculate: (i) the interest for the first year.

Explanation:

⚡ Using what you learned: compound interest

Step 1: Analyze the third question

The question asks to calculate the compound interest specifically for the second year on a principal of \( \text{₹ } 8000 \) invested for 3 years at \( 10\% \) per annum.

Step 2: Calculate interest for the first year

The principal for the first year is \( P_1 = \text{₹ } 8000 \).
The interest rate is \( R = 10\% \).

The interest for the first year (\( I_1 \)) is:

$$ I_1 = \frac{P_1 \times R \times 1}{100} = \frac{8000 \times 10 \times 1}{100} = \text{₹ } 800 $$

Step 3: Calculate principal for the second year

The principal for the second year (\( P_2 \)) is the sum of the initial principal and the interest earned in the first year:

$$ P_2 = P_1 + I_1 = 8000 + 800 = \text{₹ } 8800 $$

Step 4: Calculate interest for the second year

The interest for the second year (\( I_2 \)) is calculated on the new principal \( P_2 \):

$$ I_2 = \frac{P_2 \times R \times 1}{100} = \frac{8800 \times 10 \times 1}{100} = \text{₹ } 880 $$

Answer:

The compound interest for the second year is ₹ 880.