31. Simple and compound interest

The study of simple and compound interest is an essential part of financial mathematics and is a topic frequently covered in the National High School Exam (ENEM). To have a comprehensive understanding of this topic, it's important to understand the difference between simple and compound interest, as well as the formula used to calculate each.

Simple Interest

Simple interest is calculated based on the principal amount, that is, the initial value of the debt or investment. The formula for calculating simple interest is I = PRT, where I is the interest, P is the principal (the initial amount), R is the interest rate, and T is the time. The interest rate is usually expressed as a percentage and the time is usually expressed in years.

For example, if you invest $1,000 at an annual interest rate of 5% for 2 years, the interest you will earn will be $100 ($1,000 x 0.05 x 2). Therefore, the total amount you will have after 2 years will be $1,100 ($1,000 + $100).

Compound Interest

Compound interest, on the other hand, is calculated based on the principal amount plus the interest accrued during the period. This means you earn interest on interest, which can result in your money growing much faster compared to simple interest. The formula for calculating compound interest is A = P(1 + r/n)^(nt), where A is the amount amount, P is the principal, r is the interest rate, n is the number of times the interest is applied per period of time and t is the time.

Using the same example above, if you invest $1,000 at an annual interest rate of 5% for 2 years, but the interest is compounded annually, the total amount you will have after 2 years is $1,102.50. This is calculated as $1,000 x (1 + 0.05/1)^(1x2).

Comparing Simple and Compound Interest

The main difference between simple and compound interest is the way they are calculated. Simple interest is calculated on the principal amount only, while compound interest is calculated on the principal amount plus accrued interest. This means that over time, you'll make more money on compound interest than on simple interest.

Also, compounding frequency (that is, the number of times interest is applied) can have a big impact on the total amount you earn from compound interest. The more times interest is compounded, the more money you make.

ENEM application

At ENEM, you can expect questions involving the calculation of simple and compound interest. These questions might involve determining the total amount you will have after a certain period of time, given a certain interest rate and principal amount. In addition, you can also expect questions involving comparing simple and compound interest.

To prepare for these questions, it's important to practice using the formulas for calculating simple and compound interest and understand how compounding frequency affects the total amount you earn from compound interest.

In conclusion, the study of simple and compound interest is an essential part of financial mathematics and an important topic for ENEM. Understanding the difference between the two and how to calculate each can help you make informed financial choices and do well on the exam.

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