find the compound interest and the total amount after one year and one month if the interest is compounded quarterly principal is equal to 768 rate of interest is equal to hundred percent per annum
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Answer:
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Step-by-step explanation:
The principle of compounding growth is used extensively in the financial world to transform small savings into a big corpus over time. It’s also the underlying idea behind MBA topics such as time value of money and discounted cash flow (DCF) valuation.
Learn about simple and compound interest concepts as you’ll need them not only for entrance exams but in the real world too, especially after you become rich and famous.
Simple and Compound interest Problems and Solutions
Here is a list of some basic definition and formulas to solve problems on Interest.
Principal: This is the sum of money lent or borrowed.
Interest: This is the extra money paid for taking the money as loan. This is often expressed as a percentage.
Say, the interest is 10% on a loan of Rs. 100. Then the interest in amount is Rs. 10 and at the end of the year, the amount to be paid is Rs. 110.
Time: This is the time period for which the money is lent or the time period in which the money has to be returned with interest.
Simple Interest
As the name implies, the calculation of simple interest is pretty simple. Multiply the principal amount with the number of years and the rate of interest.
Simple Interest Formula:
Simple Interest = Principal * Time * Rate of interest / 100
Abbreviated as SI = PTR/100
Compound Interest
In compound interest, the principal amount with interest after the first unit of time becomes the principal for the next unit.
Say, when compounded annually for 2 years, the principal amount with interest accrued at the end of first year becomes the principal for the second year.
Compound Interest Formula:
Amount = Principal * [1 + Rate of Interest/100]Time period
Abbreviated as Amount = P * [1 + R/100]t, when compounded annually.
Sometimes, the interest is also calculated half-yearly or quarterly.
When compounded semi-annually or half-yearly,
Amount = P[1 + (R/2)/100]2t
When compounded quarterly,
Amount = P[1 + (R/4)/100]4t
Present worth of Principal P due t years hence is given by:
P/[1+ R/100]t
Sample problems and solutions
Let us work on some examples to understand the concepts and the differences.
Problem 1. A sum of Rs. 25000 becomes Rs. 27250 at the end of 3 years when calculated at simple interest. Find the rate of interest.
Solution:
Simple interest = 27250 – 25000 = 2250
Time = 3 years.
SI = PTR / 100 → R = SI * 100 / PT
R = 2250 * 100 / 25000 * 3 → R = 3%.
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