Question

Mindy invested $$\$ 500$$ in a savings account. After one year, her account balance was $$\$ 515$$. What percent yearly interest did her bank pay?

Short answer

The bank paid a yearly interest of \(3\%\).

Step-by-step solution

Calculate the difference in account balance

Find the difference in the account balance by subtracting the initial investment from the final account balance. Difference = Final account balance - Initial investment Difference = $$515 - 500$$

Calculate the interest

Divide the difference found in step 1 by the initial investment to get the interest as a decimal. Interest (decimal) = Difference / Initial investment Interest (decimal) = $$\frac{(515 - 500)}{500}$$

Convert decimal interest to percentage

To convert the decimal interest to a percentage, multiply the decimal interest by 100. Interest (percentage) = Interest (decimal) × 100

Calculate yearly interest percentage

Plug in the values found in steps 1 to 3 and calculate the yearly interest percentage. Difference = $$515 - 500 = 15$$ Interest (decimal) = $$\frac{15}{500} = 0.03$$ Interest (percentage) = $$0.03 × 100 = 3\%$$ The bank paid a yearly interest of $$3\%$$.

Key concepts

Interest Rate Math

Understanding interest rate math is crucial for anyone looking to invest, save money, or take out loans. Interest is the cost of using someone else's money. When you invest, you're essentially lending your money to a bank or another entity, and in return, they pay you interest. Conversely, when you take a loan, you pay interest for the privilege of using borrowed funds.

Let's break down the math using the example of Mindy, who invested \(500 in a savings account and ended up with \)515 after one year. To figure out the interest rate, first, find the increase in value: \(515 (final amount) - \)500 (initial investment) = \(15. This \)15 is the interest earned in one year. To find the interest rate, we divide the interest earned by the initial investment. So, it's \(15 / \)500 = 0.03. Since interest rates are typically expressed as percentages, we multiply the decimal by 100 to get a percentage. Thus, 0.03 \(\times\) 100 = 3%.

The equation to find the percent yearly interest is:

Basic Financial Literacy

Basic financial literacy is understanding how money works in the world: how someone manages to earn or make it, how that person manages it, how he/she invests it (turn it into more) and how that person donates it to help others. It also involves understanding financial principles and concepts like interest rates, and the ability to apply them in daily life.

The exercise with Mindy’s savings account is a fundamental example of financial literacy in action. By calculating the interest rate, anyone can gauge whether an investment is good or not. Moreover, having the knowledge to perform such calculations empowers individuals to compare different financial products, such as savings accounts, loans, or credit cards, and make informed decisions that can lead to long-term financial stability.

GED Math Preparation

DED Math Preparation involves familiarizing oneself with a variety of mathematical concepts that are necessary for earning a General Educational Development (GED) certificate. It covers arithmetic, algebra, geometry, and data analysis, which includes understanding interest rates, percentages, and financial computations.

To prepare for interest rate problems, like the one Mindy tackled, students should practice converting decimals to percentages and vice versa, along with understanding the basic algebra behind these operations. It’s not just about getting the right answer, it’s about grasping why and how the math works. A strong foundation in these mathematical concepts will aid students not only in passing their GED exam but also in handling real-life financial decisions.