Mathematics of Finance

Introduction

The mathematics of finance is a key topic in College Algebra, especially for students interested in business, economics, and the social sciences. This area focuses on the calculation and application of interest, both simple and compound, and the analysis of investments and loans.

Simple Interest

Definition and Key Concepts

• Interest is the fee charged for the use of money. It is essentially the rent paid for borrowing funds.

• Interest is usually computed as a percentage (the interest rate) of the principal over a given period of time.

• Unless otherwise stated, the interest rate is assumed to be an annual rate.

Simple Interest Formula

The formula for calculating simple interest is:

• I = interest earned or paid

• P = principal (initial amount of money)

• r = annual simple interest rate (in decimal form)

• t = time in years

Example: Calculating Simple Interest

• Problem: Compute the interest on a loan of $500 at 8% for 6 months.

• Solution: Here, , , (since 6 months is half a year).

• Substitute into the formula:

• At the end of 6 months, the borrower would repay the principal of $500 plus interest of $20, for a total of $520.

Theorem 1: Simple Interest (Future Value)

The total amount (future value) due at the end of the loan or investment period is given by:

• A = amount (future value)

• P = principal (present value)

• r = annual simple interest rate (decimal)

• t = time in years

If three of the four variables are known, the fourth can be found by rearranging the formula.

Example: Total Amount Due on a Loan

• Problem: Find the total amount due on a loan of $600 at 6% simple interest at the end of 4 months.

• Solution: , , year.

• The total amount due is $612.

Example: Present Value of an Investment

• Problem: You want to earn an annual rate of 10% on your investments. How much should you invest now to have $3,000 in 9 months?

• Solution: , , year.

• You should invest $2,790.70 now.

Simple Interest and Investments: Time in Days

• For short-term notes, time is often given in days rather than months or years.

• To convert days to years, either divide by 360 (banker's year) or by 365, as specified in the problem.

• This affects the calculation of interest for short-term investments.

Additional info:

• Simple interest is most commonly used for short-term loans or investments, such as Treasury bills or short-term notes.

• For longer-term investments, compound interest is generally used.