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# CI with a Fractional Rate

The interest rates are charged each and every time you borrow the money. Some people use simple interest while some people levy charges based on the compound interest. And today we will be discussing on compound interest. We will explain what compound interest is and solve some of the examples to help you understand the concept. There are also questions for you at the end.

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## Compound Interest

In simpler terms compound interest is explained as interest on interest. In compound interest, the interest of one year is added back into the amount and after that new interest is calculated. The following formula given below will help you calculate the amount. In the given formula, the principal amount is also given with compound interest included in it.

Source: quora.com

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

Here, P is the principal amount, R stands for rate of interest, N is for a number of years, A is the amount inclusive of principal and interest. There are other formulas used for compound interest as well for calculating interest half yearly as well as quarterly.

Compound interest for half-yearly : A = P(1 + R/100 x 2)^2N

Compound interest for quarterly: A = P(1 + R/100 x 4)^4N

If the total amount and the principal amount is given to you and you want to calculate compound interest than the formula is,
CI = A – P

## The Difference of Interest

In exams, there are questions asked where you need to find the difference between compound interest and simple interest for ‘x’ amount of years. If the difference asked is for two and three years then we have formulas with which you can calculate the difference very easily.

If the difference between compound and simple interest is asked for two years than the difference is:
P(R)²/100², where P is the principal amount and R is the rate of the interest given to us.

When the difference between compound and simple interest is asked for three years than the formula will be:
3 x P (R/100)³ + P (R/100)², here also P is the principal amount and R is the rate of interest.

### Example Based on Calculating Simple Compound Interest

1. Abhay invested Rs.1500 for a period of three years. The interest charge on the amount is 20% per annum. What will be the interest compounded annually?

A. Rs. 1060       B. Rs. 1080         C. Rs. 1092            D. Rs. 1000

Here we need to calculate the amount of 20 % compound interest charged annually. We will use the above formula to calculate this compound interest. To calculate the compound interest, the formula is,

A = P ( 1 + R/100)^N. Here, P is Rs. 1500, R is 20 % and N is 3 years. So after putting the values in the above formula, the equation will be,

A = 1500(1 + 20/100)³ => 1500(120/100)³ => 1500(1.2)³  => 1500 x 1.728
Therefore, A = 2592

Thus, the total amount compounded at the end of three years is Rs. 2592. But we need to find a compound interest that Abhay earned in these three years. So, the interest will be,

CI = A – P

Where A is the total amount and P will be the principal amount. Here A is Rs. 2592 and P are Rs. 1500. Putting these values in the above formula the result will be,

A = 2592 – 1500
A = 1092. So, the correct answer is C.

### Example Based on Calculating Amount from the Compound Interest

1. Shyam borrowed a certain sum of money and pays it back in 2 years in two equal yearly installments. The compound interest is charged at 5 % per annum and he pays back Rs. 441 every year, what was the amount that Shyam borrowed?

A. Rs. 810          B. Rs. 820          C. Rs. 840           D. Rs. 850

Here we are given the amount of interest for two years that Shyam pays. And we are required to find the total amount he borrowed. So, we need to solve this question inversely. As given in the question, the loan principal that Shyam borrowed = Present value of Rs. 441 that is payable after 1 years + present value of Rs. 441 payable after 2 years.

Thus the total amount that Shyam borrowed or the loan principal = 441/(1.05) + 441/(1.05)² = 420 + 400 = Rs. 820. So, the total amount that Shyam borrowed was Rs. 820. Thus, the correct answer is B.

## Practice Questions

1. Ajay invested half of his savings in a mutual fund that paid simple interest for 2 years and received Rs. 550 as interest. He invested the remaining in a fund that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest received Rs. 605 as interest. What was the value of his total savings before investing in these two bonds?

A. Rs. 2750        B. Rs. 2850        C. Rs. 2900         D. Rs. 2950

The correct answer is A.

2. If the simple interest is 10.5 % annual and compound interest is 10 % annual, find the difference between the interests after 3 years on a sum of Rs. 2000.

A. Rs. 30          B. Rs. 24            C. Rs. 32             D. Rs. 22

The correct answer is C.

3. What will be the compound interest at the rate of interest of 10 % for 3 years on that principle which in 3 years at the rate of 10 % per annum gives Rs? 300 as simple interest?

A. Rs. 310              B. Rs. 331              C. Rs. 333             D. Rs. 330

The correct answer is B.

4. The compound interest on Rs. 16,000 for 3 years is Rs. 2522. What will be the rate of interest?

A. 8 %           B. 6 %           C. 4 %              D. 5 %

The correct answer is D.

5. If  interest on a certain sum for 3 years at 20 % per year is Rs. 728. What would be the simple interest for the same period on the same amount?

A. Rs. 660            B. Rs. 720           C. Rs. 600              D. Rs. 690

The correct answer is C.

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##### Simple Interest and Compound Interest

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Raj

. Ajay invested half of his savings in a mutual fund that paid simple interest for 2 years and received Rs. 550 as interest. He invested the remaining in a fund that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest received Rs. 605 as interest. What was the value of his total savings before investing in these two bonds? how to solve this type of problems

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kunal kumar

2750

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Manish Rajak

5500?

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RUSHABHA KUMAR HOTA

1125 principal?

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