When I was considering what to do with my $10,000 Lottery winnings, my broker suggested I invest half of it in gold, the value of which was growing by 11% per year, and the other half in CDs, which were yielding 4% per year, compounded every 6 months. Assuming that these rates are sustained, how much will my investment be worth in 9 years? (Round your answer to the nearest cent.)

Question

When I was considering what to do with my $10,000 Lottery winnings, my broker suggested I invest half of it in gold, the value of which was growing by 11% per year, and the other half in CDs, which were yielding 4% per year, compounded every 6 months. Assuming that these rates are sustained, how much will my investment be worth in 9 years? (Round your answer to the nearest cent.)

Answer 1

^Yo that's wrong

Answer 2

To calculate the worth of your investment in 9 years, we need to calculate the future values of both the gold investment and the CD investment separately, and then add them together.

Let's start with the gold investment. The value of gold is growing by 11% per year. To calculate the future value, we can use the formula:

Future Value = Present Value * (1 + interest rate)^number of periods

In this case, the present value of your investment is $5,000 (half of your $10,000 winnings). The interest rate is 11% per year, and the number of periods is 9 years. Plugging these values into the formula:

Gold Future Value = $5,000 * (1 + 0.11)^9

Now let's calculate the future value of the CD investment. The CD has an interest rate of 4% per year, compounded every 6 months. To calculate the future value, we can use the compound interest formula:

Future Value = Present Value * (1 + interest rate / number of compounding periods)^(number of periods * number of compounding periods)

In this case, the present value of your investment is also $5,000. The interest rate is 4% per year, compounded every 6 months, so the number of compounding periods is 2 per year. The number of periods is still 9 years. Plugging these values into the formula:

CD Future Value = $5,000 * (1 + 0.04 / 2)^(9 * 2)

Now, let's calculate the future values:

Gold Future Value = $5,000 * (1 + 0.11)^9 = $5,000 * (1.11)^9 = $5,000 * 1.9994846821 = $9,997.42

CD Future Value = $5,000 * (1 + 0.04 / 2)^(9 * 2) = $5,000 * (1.02)^18 = $5,000 * 1.4323646544 = $7,161.82

Finally, adding the future values of both investments:

Investment Worth = Gold Future Value + CD Future Value = $9,997.42 + $7,161.82 = $17,159.24

Therefore, in 9 years, your investment would be worth approximately $17,159.24.

Answer 3

amount = 5000(1.11)^9 + 5000(1.02)^18

= ...
you do the button-pushing