What is the difference between the compound interest and the simple interest for the sum Rs. 16000 at 5% p.a. for 2 years?a)Rs. 80b)Rs. 60c)Rs. 54d)Rs. 40e)Rs. 35Correct answer is option 'A'. Can you explain this answer?

Question

Answer

Option ( A) 40 is the correct answer.

Explanation:- Given, P = 16000₹

R = 5% , T = 2 years

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

= 16000 * ( 1+5/100) ^2

= 16000 * ( 105 / 100) ^2

A = 17,640₹

C. I = A- P

= 17,640 - 16,000

= 1,640

S. I = PTR / 100

= 16000 * 2 * 5/ 100

= 1,600

Difference CI - SI ;

= 1640 - 1600

= 40 ₹

Answer

1). Method PR^2/(100)^2 = 16000 × 25/100 × 100 = 40 So ans D. ...............
2). Method = 5% of 16000 = 16000×1/20 - 800 and again 5% of 800 = 800×1/20 = 40 Ans..
3). Method- Direct P(1+r/t)^n -PRT/100 = 40 Ans...
4). Method Percentage effect x + y +xy/100 = 5+5+5×5/100 = 10.25%. so increased percentage = 0.25% = 16000× 0.25/100 = 40 Ans.
5). Also.. want to know

Answer

Given information:
Principal amount (P) = Rs. 16000
Rate of interest (R) = 5% per annum
Time period (T) = 2 years

Simple Interest (SI) formula:
SI = (P * R * T) / 100

Compound Interest (CI) formula:
CI = P * (1 + R/100)^T - P

Calculating Simple Interest:
SI = (16000 * 5 * 2) / 100
SI = 1600

Calculating Compound Interest:
CI = 16000 * (1 + 5/100)^2 - 16000
CI = 16000 * (1.05)^2 - 16000
CI = 16000 * 1.1025 - 16000
CI = 17640 - 16000
CI = 1640

Difference between Compound Interest and Simple Interest:
Difference = CI - SI
Difference = 1640 - 1600
Difference = 40

Therefore, the difference between the compound interest and the simple interest for the sum of Rs. 16000 at 5% p.a. for 2 years is Rs. 40.

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