Mr. Singh Has Rs 500, Which He Invested For 3 Years At The Rate Of $6 \%$ Per Annum.i. Find The Interest For 1 Year.ii. Find The Total Interest For The Entire Period.iii. Find The Amount If He Withdraws At The End Of 2 Years.

Feb 27, 2025 by ADMIN 228 views

Understanding Simple Interest and Compound Interest

Calculating Interest for 1 Year

Mr. Singh's Investment Scenario

Mr. Singh has invested Rs 500 for a period of 3 years at an annual interest rate of 6%. To find the interest for 1 year, we can use the simple interest formula:

Simple Interest Formula:

${ \text{Simple Interest} = \frac{P \times R \times T}{100} }$

Where:

${ P }$ is the principal amount (initial investment)
${ R }$ is the annual interest rate (in %)
${ T }$ is the time period (in years)

Applying the Formula:

${ \text{Simple Interest for 1 year} = \frac{500 \times 6 \times 1}{100} }$ ${ \text{Simple Interest for 1 year} = \frac{3000}{100} }$ ${ \text{Simple Interest for 1 year} = 30 }$

Therefore, the interest for 1 year is Rs 30.

Calculating Total Interest for the Entire Period

Calculating Compound Interest

To find the total interest for the entire period, we can use the compound interest formula:

Compound Interest Formula:

${ A = P \left( 1 + \frac{R}{100} \right)^T }$

Where:

${ A }$ is the amount after the time period
${ P }$ is the principal amount (initial investment)
${ R }$ is the annual interest rate (in %)
${ T }$ is the time period (in years)

Applying the Formula:

${ A = 500 \left( 1 + \frac{6}{100} \right)^3 }$ ${ A = 500 \left( 1 + 0.06 \right)^3 }$ ${ A = 500 \left( 1.06 \right)^3 }$ ${ A = 500 \times 1.191016 }$ ${ A = 595.508 }$

The amount after 3 years is Rs 595.508.

Calculating Total Interest:

To find the total interest, we subtract the principal amount from the amount after 3 years:

${ \text{Total Interest} = A - P }$ ${ \text{Total Interest} = 595.508 - 500 }$ ${ \text{Total Interest} = 95.508 }$

Therefore, the total interest for the entire period is Rs 95.508.

Calculating the Amount if Withdrawn at the End of 2 Years

Calculating Compound Interest for 2 Years

To find the amount if withdrawn at the end of 2 years, we can use the compound interest formula for 2 years:

Compound Interest Formula for 2 Years:

${ A = P \left( 1 + \frac{R}{100} \right)^T }$

Where:

${ A }$ is the amount after the time period
${ P }$ is the principal amount (initial investment)
${ R }$ is the annual interest rate (in %)
${ T }$ is the time period (in years)

Applying the Formula:

${ A = 500 \left( 1 + \frac{6}{100} \right)^2 }$ ${ A = 500 \left( 1 + 0.06 \right)^2 }$ ${ A = 500 \left( 1.06 \right)^2 }$ ${ A = 500 \times 1.1236 }$ ${ A = 561.8 }$

The amount after 2 years is Rs 561.8.

Therefore, if Mr. Singh withdraws his investment at the end of 2 years, he will receive Rs 561.8.
Frequently Asked Questions (FAQs) on Simple and Compound Interest

Q1: What is the difference between simple interest and compound interest?

A1: Simple interest is calculated only on the initial principal amount, whereas compound interest is calculated on the initial principal amount and any accrued interest.

Q2: How is simple interest calculated?

A2: Simple interest is calculated using the formula: Simple Interest = (P × R × T) / 100, where P is the principal amount, R is the annual interest rate, and T is the time period.

Q3: How is compound interest calculated?

A3: Compound interest is calculated using the formula: A = P (1 + R/100)^T, where A is the amount after the time period, P is the principal amount, R is the annual interest rate, and T is the time period.

Q4: What is the formula for calculating the amount after a certain period of time?

A4: The formula for calculating the amount after a certain period of time is: A = P (1 + R/100)^T, where A is the amount after the time period, P is the principal amount, R is the annual interest rate, and T is the time period.

Q5: How do I calculate the total interest earned on an investment?

A5: To calculate the total interest earned on an investment, you can subtract the principal amount from the amount after the time period: Total Interest = A - P, where A is the amount after the time period and P is the principal amount.

Q6: What is the formula for calculating the amount if withdrawn at the end of a certain period of time?

A6: The formula for calculating the amount if withdrawn at the end of a certain period of time is: A = P (1 + R/100)^T, where A is the amount after the time period, P is the principal amount, R is the annual interest rate, and T is the time period.

Q7: How do I calculate the interest for a specific period of time?

A7: To calculate the interest for a specific period of time, you can use the simple interest formula: Simple Interest = (P × R × T) / 100, where P is the principal amount, R is the annual interest rate, and T is the time period.

Q8: What is the difference between annual percentage rate (APR) and annual percentage yield (APY)?

A8: APR is the interest rate charged on a loan or credit product, while APY is the rate of return on an investment. APY takes into account the compounding effect of interest.

Q9: How do I calculate the future value of an investment?

A9: To calculate the future value of an investment, you can use the formula: FV = PV (1 + R/100)^T, where FV is the future value, PV is the present value (principal amount), R is the annual interest rate, and T is the time period.

Q10: What is the formula for calculating the present value of a future amount?

A10: The formula for calculating the present value of a future amount is: PV = FV / (1 + R/100)^T, where PV is the present value, FV is the future value, R is the annual interest rate, and T is the time period.

We hope these FAQs have helped you understand simple and compound interest better. If you have any more questions, feel free to ask!