Step-by-Step Guide: Business Mathematics Chapter 7 Solutions

Introduction

Business Mathematics Chapter 7 is a crucial component of any business course, covering topics such as compound interest, annuities, and amortization. These concepts are essential to understanding the financial operations of any business, and it is crucial to have a clear understanding of the solutions to these mathematical problems. In this article, we will provide a step-by-step guide to solving the problems in Business Mathematics Chapter 7, along with examples and case studies to help you understand the concepts better.

Compound Interest

One of the most important concepts covered in Chapter 7 is compound interest. Compound interest is the interest calculated on the principal amount plus any accumulated interest. The formula for calculating compound interest is A=P(1+r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest compounds each year, and t is the time in years.

Let’s take an example to understand this better. Suppose you invest $10,000 in a savings account that pays an annual interest rate of 4.5%, compounded monthly for three years. To calculate the final amount, we can use the formula mentioned above:

A= $10,000 ( 1+ 0.045 / 12 ) ^(12 x 3)

A= $11,522.39

Therefore, after three years, the final amount would be $11,522.39.

Annuities

Another important concept in Chapter 7 is annuities. An annuity is a fixed sum of money paid to someone each year, typically for the rest of their life. There are two types of annuities – ordinary annuity and annuity due.

The formula for calculating the present value of an ordinary annuity is P= PMT x (1- (1/ (1+r)^n))/ r, where P is the present value, PMT is the annuity payment amount, r is the annual interest rate, and n is the number of payments.

Let’s take an example to understand this better. Suppose you want to invest in an annuity that pays $1,000 per annum for 5 years, and the annual interest rate is 5%. To calculate the present value of the annuity, we can use the formula mentioned above:

P= $1,000 x (1- (1/ (1+0.05)^5))/0.05

P= $4,329.48

Therefore, to receive $1,000 per annum for five years, you would need to invest $4,329.48.

Amortization

Amortization is the process of reducing debt by making regular payments of principal and interest. The formula for calculating the periodic payment amount is PMT = (PV x r) / (1 – (1 + r)^-n), where PV is the present value, r is the interest rate, and n is the number of payments.

Let’s take an example to understand this better. Suppose you have a loan of $50,000, with an annual interest rate of 6%, and you need to repay it over ten years, making monthly payments. To calculate the monthly payment, we can use the formula mentioned above:

PMT= ($50,000 x 0.005) / (1- (1+ 0.005)^-120)

PMT= $555.10

Therefore, to repay the loan over ten years, you need to make a monthly payment of $555.10.

Conclusion

In conclusion, Business Mathematics Chapter 7 is an essential component of any business course. Understanding the solutions to the mathematical problems covered in this chapter is crucial for any individual or business that deals with finances. In this article, we provided a step-by-step guide to solving the problems in Chapter 7, along with examples and case studies to help you understand the concepts better. We hope this article was informative and useful for you.