Question

you are scheduled to receive $5,000 in two years. when you receive it, you will invest it at 6.5 percent per year. how much will your investment be worth eight years from now?

Answer 1

To calculate the future value of a $5,000 investment at a 6.5% annual interest rate over six years (since the investment starts two years from now and the total timeframe is eight years), you use the compound interest formula A = P(1 + r/n)^(nt).

Step-by-step explanation:

If you are scheduled to receive $5,000 in two years and plan to invest it at a 6.5 percent annual interest rate, to find out how much the investment will be worth in eight years, you can use the formula for compound interest. The formula is A = P(1 + r/n)^(nt), where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (decimal).
• n is the number of times that interest is compounded per year.
• t is the time the money is invested for in years.

In this case, since you will invest your money right after you receive it, which is in two years, and want to know the value in eight years, you should calculate the investment over six years. Since the interest is compounded annually, n is 1. Thus, the equation becomes A = $5,000(1 + 0.065/1)^(1*6), which simplifies to A = $5,000(1 + 0.065)^6. After calculating, you will get the future value of your investment.

Answer 2

The investment of $5,000 at 6.5% annual interest compounded annually will be worth approximately $9,484.31 after ten years. to find how much the investment will be worth in eight years, we must couant the total investment period as ten years (two years until you receive the money plus the eight years of investment).

Step-by-step explanation:

The question involves calculating the future value of a single investment using compound interest. Since you are scheduled to receive $5,000 in two years and intend to invest that amount at 6.5% per year, to find how much the investment will be worth in eight years, we must count the total investment period as ten years (two years until you receive the money plus the eight years of investment).

The formula for compound interest is A = P(1 + r/n)^(nt), where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (decimal).
• n is the number of times that interest is compounded per year.
• t is the time the money is invested for in years.

Assuming that the interest is compounded once per year (n=1), the formula simplifies to A = P(1 + r)^t. In this case, P = $5,000, r = 0.065 (6.5%), and t = 10 years.

Therefore, the future value of the investment will be:

A = $5,000(1 + 0.065)^10

A = $5,000(1.065)^10

A = $5,000 * 1.896862

A ≈ $9,484.31

After ten years, your investment will be worth approximately $9,484.31.