If a sum is lent at 5% compound interest per annum for 2 yr. What is the ratio of the amount to the principal?a)441 : 400b)400 : 441c)399 : 400d)None of theseCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

Given:
- Sum is lent at 5% compound interest per annum for 2 years.

To find:
- The ratio of the amount to the principal.

Solution:
Let's assume the principal amount is P.

Calculation:
The compound interest formula is given by:
Amount = Principal * (1 + Rate/100)^Time

For the given problem, the rate is 5% and the time is 2 years.
So, the amount after 2 years will be:
Amount = P * (1 + 5/100)^2
= P * (1.05)^2
= P * 1.1025

The ratio of the amount to the principal will be:
Amount/Principal = P * 1.1025 / P
= 1.1025

Simplifying the ratio, we get:
Amount/Principal = 110.25/100
= 441/400

Therefore, the required ratio of the amount to the principal is 441 : 400.

Hence, the correct answer is option A) 441 : 400.

Similar Teaching Doubts

A person lent Rs. 5,000 partly at the rate of 4 percent and partly at the rate of 5 percent per annum, at simple interest for purchased a wristwatch. The total interest after 2 years is Rs. 440. The sum of money lent at each of the above rates is to be divided in the ratio

The compound interest on Rs.36000 lent at 10 % per annum for 2.5 years, if the interest is compound annually, is

A person lent certain sum of money at 5% per annum simple interest and in 15 years the interest amounted to Rs 500 less than the sum lent. What was the sum lent?

The difference of compound interest and simple interest for 3 years and for 2 years are in ratio 23: 7 respectively. What is rate of interest per annum (in %)?

Mr. X invested an amount for 2 years at 15% per annum at simple interest. Had the interest been compounded, he would have earned Rs. 450/- more as interest. What was the amount invested?

Top Courses for Teaching

Suggested Free Tests

Related Content

Schools

Competitive Examinations

Quick Access Links

Technical Exams