Question

Claudette's cash. Claudette invested one-half of her inheritance in a CD paying 5%, one-third in a mutual fund paying 6%, and spent the rest on a new car.

Answer 1

Simple interest and compound interest calculations involve formulas that take into account the principle, rate, and time. For compound interest, the formula A = P(1 + r)^n is used. High risk in investments does not inherently mean low returns, as it represents potential for both high and low outcomes.

Step-by-step explanation:

Claudette's situation involves financial decisions such as investment and spending. To address some related concepts:

Calculating Interest from a Loan

For the total amount of simple interest from a $5,000 loan after three years at a simple interest rate of 6%, we use the formula I = Prt, where I is the interest, P is the principal amount, r is the rate of interest per year, and t is the time in years. Therefore, I = $5,000 * 0.06 * 3 = $900.

Determining Interest Rate

For the interest rate charged on a $10,000 loan upon receiving $500 in simple interest over five years, we rearrange the simple interest formula to r = I / (Pt). Hence, r = $500 / ($10,000 * 5) = 0.01 or 1% per annum.

Calculating Compound Interest

To find the value of a 5-year CD for $1,000 with a 2% annual compound interest rate, we use the formula A = P(1 + r)^n, where A is the amount, P is the principal, r is the annual interest rate, and n is the number of years. After calculating, A = $1,000(1 + 0.02)^5 ≈ $1,104.08.

Understanding Investment Returns

When comparing the average return over time between stocks, bonds, and a savings account, stocks tend to have a higher average return despite being more volatile. Bonds generally offer moderate returns with lower risk compared to stocks. A savings account usually provides the lowest return but is the safest investment.

Myth of High-risk and Low-return

The notion that a high-risk investment must yield a low return is not accurate. High risk can lead to both high or low returns, as risk is an inherent part of investing and reflects the potential variation in returns.

Answer 2

The questions involve understanding investments and the concept of compound interest. Stocks typically offer higher average returns than bonds or savings accounts due to their higher risk. Calculating simple and compound interest allows us to determine the total amount of interest earned or owed, and the future value of investments respectively.

Step-by-step explanation:

Understanding Compound Interest and Investments

To comprehend the scenarios given, we must grasp the principles of compound interest and investment returns. For Claudette's cash scenario, we are looking at different investment vehicles and their rates but we need more information to assess the outcome. When it comes to investment returns, historically, stocks have had a higher average return compared to bonds and savings accounts. This is attributable to their higher risk levels which often correlate with potentially higher rewards.

Considering the cases of Freda and Frank, we observe two different property transactions with implied capital gains. In Freda's case, her property appreciated from $150,000 to $250,000, while Frank's went from $100,000 to $160,000, after making a down payment and repaying some of his bank loan.

Regarding the fear that high-risk investment opportunities lead to low returns, this is a misconception. High risk correlates with the potential for both high and low returns; it is the uncertainty that is high, not necessarily the outcome of low returns. In terms of simple interest, for a $5,000 loan at 6% over three years, the total interest would be $900. For the second interest calculation, an interest of $500 on a $10,000 loan over five years indicates an annual interest rate of 1%.

Finally, to understand the future value of a compound interest investment, we can consider a 5-year CD with a principal amount of $1,000 and an annual interest rate of 2%. Using the compound interest formula, the value of the CD at the end of five years would be $1,104.08.

As for methods used by start-up firms to raise financial capital, the most common ways include venture capital, angel investors, crowdfunding, and small business loans.