Question

You have $12 000 in cash. You can deposit it today in an investment fund earning 8.2 per cent semiannually, or you can wait, enjoy some of it, and invest $11 000 in your brother’s business in 2 years. Your brother is promising you a return of at least 10 per cent on your investment. Whichever alternative you choose, you will need to cash in at the end of 10 years. Assume your brother is trustworthy and both investments carry the same risk. Which one will you choose?

Answer 1

Calculating the future value of both options shows that the investment fund yielding 8.2% compounded semiannually results in approximately $26,635.68, whereas the investment in your brother's business at 10% annual interest results in approximately $23,579.49 after 10 years. Therefore, the investment fund is the better choice.

Step-by-step explanation:

To determine which investment would result in a greater amount at the end of 10 years, we must calculate the future value of both the investment fund option and your brother's business investment.

Investment Fund Calculation:

The investment fund compounds semiannually at 8.2% interest. The future value (FV) formula for compound interest is:

FV = P(1 + r/n)^(nt)

Where:

• P is the principal amount ($12,000)
• r is the annual interest rate (0.082)
• n is the number of times interest is compounded per year (2)
• t is the number of years the money is invested (10)

FV = $12,000(1 + 0.082/2)²ˣ¹⁰

FV = $12,000(1 + 0.041)²⁰

FV = $12,000(1.041)²⁰

FV = $12,000 * 2.21964

FV ≈ $26,635.68

Brother's Business Calculation:

The investment in your brother's business will be $11,000 after 2 years with an assumed interest of at least 10%. So the formula becomes:

FV = P(1 + r)^(t)

Where:

• P is the principal amount ($11,000)
• r is the annual interest rate (0.10)
• t is the number of years the money is invested (10 - 2 = 8)

FV = $11,000(1 + 0.10)⁸

FV = $11,000(1.10)⁸

FV = $11,000 * 2.14359

FV ≈ $23,579.49

Comparing the two, the investment fund with semiannual compounding yields a higher amount at the end of 10 years than investing in your brother's business, with amounts of approximately $26,635.68 and $23,579.49, respectively.

Answer 2

You are better off investing today in the mutual fund and earn 8.2 percent semiannually for 10 years.

Step-by-step explanation:

We will need to calculate the interest generated in both of these scenarios to determine which one is the best.

In scenario 1

Periods= 10 years * 2= 20 periods (since rate is biannual)

Principal= $12,000

Rate= 8.2%

Using the formula

Interest= Principal * Rate * Time

Interest= 12,000* 0.082 * 20

Interest= $19,680

In scenario 2

Principal= $11,000

Rate= 10%

Period= 8 years ( two years have already passed, so we calculate for 8 years since we want to see gain after 10 years)

Interest= 11,000* 0.10 * 8

Interest= $8,800

So imvesting $12,000 at interest rate of 8.2% biannually for 10 years is a better option.