Compound Interest

Jojo had just learnt the concept of Simple and Compound Interest in his Mathematical classes. While doing his homework something struck him and he immediately went and asked this question to his father: “What would be the final amount for a principal deposit of Rs.1000, time duration of one year, if 10% interest is compounded continuously?” His father was a Bank Officer who had an experience in the banking service which was more than Jojo’s age and he still could not answer the question.

Can you help the smart Jojo to get his doubt cleared?


Hint 1

If you do not know how to start, there is a formula for finding the compound interest. Use the formula.


Hint 2

The answer is finite. If you do not know how to proceed with the formula, try using some limit concepts.


Answer

Rs.1105


Solution

From the problem it is very clear that the problem is a problem in compound interest. We know that the formula for compound interest is
























According to our problem,




We cannot just substitute the above values into the formula directly as k is infinite. So we need to find






Let the above expression be represented by L. Therefore



















On substituting the values, we have







The final amount for the principal deposit of Rs.1000 at a rate of interest 10% for time duration of 1 year if the interest is compounded continuously is Rs.1105. This solves the problem of Jojo.

For different values of k for the above problem, we have

k	1	12	52	365	8760	Inf
Final Amount	1100	1104.713	1105.065	1105.158	1105.170	1105.171

As we can judge from the above table the interest added when k increases becomes negligibly small. If you open a bank, you can make a new scheme telling the customers that you compound interest continuously and this attracts more customers. Try it out.