Question

One year ago Harold invested $$\$ 24,000$$ in a bank bond that offers \(3 \%\) annual interest. At the same time, Maude invested \(\frac{1}{3}\) that amount in a fund that produced an annual yield of \(8 \%\). At the end of the year, what was the difference between Harold's interest earnings and Maude's gains from her investment yield? A. $$\$ 80$$ B. $$\$ 240$$ C. $$\$ 640$$ D. $$\$ 5,040$$

Short answer

A. $$\$ 80$$

Step-by-step solution

Understanding the given information

Harold invested $$\$ 24,000$$ in a bank bond with an annual interest rate of \(3 \%\). Maude invested $$\frac{1}{3}$$ of Harold's investment ($$\frac{1}{3}\times \$ 24,000$$) in a fund with an \(8 \%\) annual yield.

Calculate Harold's interest earnings

To find the interest earned by Harold, multiply the principal (\(\$ 24,000\)) by the interest rate (\(3 \%\)) and convert that to a decimal. Interest earned = $$(\$24,000) \times (0.03)$$

Calculate Maude's investment amount and gains

First, we need to find the amount Maude invested by multiplying Harold's investment by $$\frac{1}{3}$$. Maude's investment = $$(\$ 24,000)\times\frac{1}{3}$$ Now, calculate the gains earned by Maude by multiplying her investment by the annual yield converted to a decimal. Maude's gains = (Maude's investment) × (0.08)

Find the difference between Harold's and Maude's earnings

Subtract Maude's gains from Harold's interest earnings to find the difference. Difference = (Harold's interest earnings) - (Maude's gains)

Perform calculations and choose the correct answer

Harold's Interest earnings = $$(\$24,000) \times (0.03) = \$720$$ Maude's investment = $$(\$ 24,000)\times\frac{1}{3} = \$ 8,000$$ Maude's gains = (\(\$8,000) × (0.08) = \$640\) Difference = (\(\$720) - (\$640) = \$80\) The difference between Harold's interest earnings and Maude's gains from her investment yield is $$\$80$$. The correct answer is A. $$\$ 80$$.

Key concepts

Simple Interest Calculation

When it comes to understanding financial math, getting a grip on simple interest calculations is a great starting point. Simple interest is determined by multiplying the principal amount, the interest rate (as a decimal), and the time (usually in years). The formula looks like this: \begin{align*}\text{Simple Interest} = \text{Principal} \times \text{Interest Rate} \times \text{Time}d{align*}Translating percentages to decimals involves moving the decimal point two places to the left. For example, a 3% interest rate becomes 0.03 in the formula. To practice, let’s imagine you deposit \(1,000 at a 5% interest rate for one year. Using the formula, your simple interest earned would be:\begin{align*}\text{Simple Interest} = 1000 \times 0.05 \times 1 = \)50d{align*}Understanding this will give you a solid foundation for comparing investments and figuring out which is more beneficial—as seen in Harold and Maude's scenario.

Investment Comparison

Comparing different investment opportunities can be crucial for making informed financial decisions. Key variables in this comparison include the amount of the initial investment, the interest rate or yield, and the time frame.

Variables to Consider

• Principal: The initial amount invested.
• Rate of Return: The percentage at which the investment increases - interest rate for a bond or yield for other investments.
• Duration: The time over which the investment grows.

In our textbook example, Harold and Maude invested different amounts at different rates of return for the same duration. When comparing such investments, always keep in mind how each variable may affect the end result. Calculating simple interest for both scenarios reveals that despite different rates, the actual monetary difference in gains can be surprisingly modest.

Percentage Yield

Percentage yield refers to the earnings from an investment over a specific period, expressed as a percentage of the original investment. Unlike simple interest that is calculated only on the principal, percentage yield can also apply to compound interest, where the interest earned each period is added to the principal.

Translating Yield to Earnings

To convert a yield into actual earnings:

1. Express the yield as a decimal by dividing the percentage by 100.
2. Multiply the decimal yield by the total investment amount.

In the case of Maude, with an 8% yield on her \(8,000 investment, her earnings were calculated as:\begin{align*}\text{Maude's gains} = (\text{Investment amount}) \times \text{Yield} = (8000) \times 0.08 = \)640d{align*}This concept becomes particularly valuable when assessing the relative advantage of different investment vehicles.

GED Math Practice

The General Educational Development (GED) tests are a suite of four subject tests which, when passed, certify that the test taker has American or Canadian high school-level academic skills. One of the subjects is mathematics, which covers algebra, geometry, and data analysis, with real-world problems requiring applicants to demonstrate understanding and application of mathematical concepts.

Key Areas

• Numerical operations and number sense.
• Measurement and geometry.
• Data analysis, statistics, and probability.
• Algebra functions and patterns.

The textbook scenario with Harold and Maude, involving interest rates and percentage yields, is the kind of real-life application that could appear in a GED math test. These tests assess not just mathematical operations but also problem-solving and critical thinking skills, using practical examples. Solving such problems successfully is a testament to a good understanding of fundamental math concepts and their applications in everyday situations.