Mastering 11th Business Maths Exercise 5.5 with Step-by-Step Solutions

Mastering 11th Business Maths Exercise 5.5 with Step-by-Step Solutions

Business Mathematics is an important subject that has great relevance in today’s corporate world. As a student, mastering the fundamentals of business mathematics can be a strenuous task, but with dedication and practice, it can become an easy and rewarding task. In this article, we will explore and delve into the world of business maths exercise 5.5, with step-by-step solutions.

Exercise 5.5 in business maths deals with compound interest and growth. It is one of the most important topics that students come across in their 11th standard. Learning about the compounding of interest and growth can be a daunting task, as it involves calculations that require careful attention to detail. Let’s dive in and understand the concepts of compound interest and growth with the help of some examples.

Understanding Compound Interest:

Compound interest is interest that is calculated on the principal amount as well as the accumulated interest of previous periods. This type of interest has the potential to give greater returns in the long run, as compared to simple interest. To understand the concept of compounding interest, let’s take a look at an example.

Suppose you have invested Rs.1000 in a bank account with an annual interest rate of 10% for 5 years. The interest is compounded annually, which means that at the end of one year, you will have Rs. 1100 (1000 principal + 100 interest). At the end of the second year, you will have Rs.1210 (1100 principal + 110 interest). This process continues till the end of the fifth year, where you will end up with Rs. 1610 (1000 principal + 610 interest). You would have earned Rs. 610 as interest over 5 years, which is much higher than what you would have earned with simple interest.

Solving Exercise 5.5:

Now that we understand the concept of compound interest, let’s take a look at how to solve exercise 5.5 step-by-step. The first step is to identify the principal amount, interest rate, and the time period for which the interest is being compounded. Once that is done, calculate the compound amount (principal + interest) for each year. The formula to calculate the compound amount is:

Compound Amount = Principal x (1 + (Rate/100))^Time

Once you have calculated the compound amount for each year, subtract the principal amount from the compound amount to get the interest earned for that year. Finally, add up the interest earned for all the years to get the total interest earned.

Example:

Suppose you have invested Rs.5000 in a bank account with an annual interest rate of 12%, compounded every six months for three years.

– Principal amount – Rs.5000
– Interest rate – 12%
– Time period – 3 years
– Compounding period – Every six months

Step 1: Calculate half-yearly interest rate:

Half-yearly rate = 12/2 = 6%

Step 2: Calculate the compound amount:

Compound amount for the first six months = Rs.5000 x (1+(6/100))^1
= Rs.5300

Compound amount for the second six months = Rs.5300 x (1+(6/100))^1
= Rs.5618

Similarly, we can calculate the compound amount for the remaining two and a half years.

Step 3: Calculate the interest earned:

Interest earned for the first six months = Compound amount for the first six months – Principal
= Rs.300

Similarly, we can calculate the interest earned for all the six-monthly periods.

Step 4: Calculate the total interest earned:

Total interest earned = Interest earned for first six months + Interest earned for the next six months + … + Interest earned for the last six months
= Rs.1928

Conclusion:

Mastering exercise 5.5 of business maths can be a challenging task, but with practice and patience, it can be achieved. The key to success is to understand the concept of compounding, and to approach the exercise systematically. To solve the exercise efficiently, it is best to identify the principal amount, interest rate, compounding period, and time period correctly. Once these variables have been identified, solving the exercise becomes a matter of using the right formulae and applying the correct calculation techniques.

In conclusion, compounding is a powerful tool, and understanding the concept is essential in mastering business mathematics. By applying the techniques and formulas discussed in this article, students can gain a clear understanding of compound interest and growth, and tackle exercise 5.5 with ease. Happy learning!