Question

The difference between the compound interest compounded half yearly and yearly on a sum of money for 2 years at the rate of 20% p.a. is Rs 289.20. a) Find the sum. b) Find the compound interest compounded annually. c) Find the compound interest compounded semi-annually. d) By what percent is the interest compounded annually is less than the interest compounded semi-annually?​

Answer 1

Answer: (A): Rs 4000, (B): Rs 1760, (C): Rs 2049.20, (D): 16.42% Less

(A) -The SUM is Rs 4000

(B) -The Compound Interest Compounded Annually is Rs 1760

(C) -The Compound Interest Compounded SEMI-ANNUALLY is

Rs 2049.20

(D) -The Interest Compounded Annually is 16.42% LESS than the interest Compounded SEMI-ANNUALLY.

• Explanation:

• MAKE A PLAN:

Let us Denote the SUM as P: We will find the compound interest compounded annually and semi-annually, and then calculate the difference between them:

• SOLVE THE PROBLEM:

• (A) - FIND THE SUM:

• (1) - Compound Interest Compounded Annually Formula:

A = P(1 + R/100)^n

• (2) - Compound Interest Compounded Semi-Annually Formula:

A = P(1 + R/2 * 100)^2n

• (3) - Difference Between Compound Interest:

P(1 + R/2 * 100)^2n - P(1 + R/100)^n = 289.20

• (4) - PLUG THE GIVEN VALUES IN:

P(1 + 20/2 * 100)^2 * 2 - P(1 + 20/100)^2 = 289.20

• (5) - SOLVE FOR P:

P = 4000

• (B) - FIND THE COMPOUND INTEREST COMPOUNDED ANNUALLY:

• (1) - Calculate the amount After TWO (2) Years:

A = 4000(1 + 20/100)^2 = 5760

• (2) CALCULATE THE COMPOUND INTEREST:

CI = A - P

= 6049.20 - 4000

= 2049.20

• (D) - By what Percent (%) is the interest Compounded Annually, LESS than the Interest Compounded SEMI-ANNUALLY?

• (1) - Calculate The DIFFERENCE in INTEREST:

2049.20 - 1760 = 289.20

• (2) - Calculate the PERCENTAGE (%) DIFFERENCE:

289.20 / 1760 * 100 = 16.42%

• DRAW THE CONCLUSION:

(A) -The SUM is Rs 4000

(B) -The Compound Interest Compounded Annually is Rs 1760

(C) -The Compound Interest Compounded SEMI-ANNUALLY is

Rs 2049.20

(D) -The Interest Compounded Annually is 16.42% LESS than the interest Compounded SEMI-ANNUALLY.

I hope this Helps You!