Question

if the compound interest on a sum of money compounded semi annually in one year at 10%per annum is rs.40 more than the compound interest on the same sum compounded annually in the same time and the same rate, find the sum.​

Answer 1

Answer (1) - Therefore, The Sum of Money is Rs.2000

Answer (2) - Therefore the Sum Of Money is Rs. 16000

• STEP By STEP EXPLANATION:

Make A Plan:

Let's Denote the sum as P. We will use the compound interest formula to find the difference between the compound interest compounded semi-annually and annually.

• SOLVE THE PROBLEM:

1) - Compound Interest Compounded Semi-Annually

A1 = P(1 + 0.1/2)^2*1 = P = 1.05)^2

2) - Compound Interest compounded annually:

A2 = P(1 + 0.1)^1 = P(1.1)

3) - The Difference between compound Interests is

Rs. 40

A1 - A2 = 40

4) - Substitute the Expressions for A1 and A2

P(1.05)^2 - P(1.1) = 40

5) - Factor Out P:

P((1.05)^2 - 1.1 ) = 40

6) - SOLVE FOR P:

P = 40/(1.05)^2 - 1.1

P = 2000

Draw the conclusion:

Therefore, The Sum of Money is Rs.2000

STEP By STEP Explanation TWO(2):

Let the sum is Rs X

x( 1 + 10% /2)^2 - 40 = x( 1 + 10%)^1

1.1025 X - 40 = 1.1 X

1.1025 X - 1.1 X = 40

0.0025 X = 40

So, X = 16000

• Draw Conclusion:

Therefore the Sum Of Money is Rs. 16000

I hope this helps!

Answer 2

16,000.

Explanation:

Let's denote the principal sum of money as P.

The compound interest on the sum compounded semi-annually in one year at 10% per annum can be calculated using the formula:

A₁ = P(1 + r/n)^(nt)

Where:

A₁ is the amount after one year, r is the annual interest rate (10% or 0.10), n is the number of times interest is compounded per year (2 for semi-annual compounding), and t is the number of years (1 in this case).

Similarly, the compound interest on the sum compounded annually in one year at the same rate can be calculated using the formula:

A₂ = P(1 + r)^t

Given that the compound interest compounded semi-annually is Rs.40 more than the compound interest compounded annually, we can set up the equation:

A₁ - A₂ = 40

P(1 + r/n)^(nt) - P(1 + r)^t = 40

Now let's substitute the values into the equation:

P(1 + 0.10/2)^(2*1) - P(1 + 0.10)^1 = 40

P(1 + 0.05)^2 - P(1 + 0.10) = 40

P(1.05)^2 - P(1.10) = 40

1.1025P - 1.10P = 40

0.0025P = 40

P = 40 / 0.0025

P = 16,000

Therefore, the principal sum of money is Rs. 16,000.