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 12% per year, and the other half in CDs, which were yielding 5% per year, compounded every 6 months. Assuming that these rates are sustained, how much will my investment be worth in 7 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 12% per year, and the other half in CDs, which were yielding 5% per year, compounded every 6 months. Assuming that these rates are sustained, how much will my investment be worth in 7 years? (Round your answer to the nearest cent.)

Answer 1

To calculate the worth of your investment in 7 years, we need to calculate the future value of the two separate investments and then add them together.

First, let's calculate the worth of the investment in gold. We can use the compound interest formula:

FV = PV * (1 + r)^n

Where:
FV = Future Value
PV = Present Value (initial investment)
r = Interest rate per compounding period
n = Number of compounding periods

In this case, the initial investment in gold is $5,000 and the interest rate is 12% per year. Since it's compounded annually, there is only one compounding period per year. So we can plug these values into the formula:

FV_gold = $5,000 * (1 + 0.12)^7

Calculating this, we find the future value of the investment in gold after 7 years is $11,318.92.

Next, let's calculate the worth of the investment in CDs. The interest on CDs is compounded every 6 months, which means there are two compounding periods per year. The formula for compound interest with multiple compounding periods per year is:

FV = PV * (1 + r/n)^(n*t)

Where:
FV = Future Value
PV = Present Value (initial investment)
r = Interest rate per year
n = Number of compounding periods per year
t = Number of years

In this case, the initial investment in CDs is also $5,000 and the interest rate is 5% per year. Since it's compounded every 6 months, there are two compounding periods per year. So we can plug these values into the formula:

FV_CDs = $5,000 * (1 + 0.05/2)^(2*7)

Calculating this, we find the future value of the investment in CDs after 7 years is $6,381.51.

Now, we can calculate the total worth of your investment by adding the future values of the two investments together:

Total_FV = FV_gold + FV_CDs
Total_FV = $11,318.92 + $6,381.51

Calculating this, we find that the total worth of your investment in 7 years will be $17,700.43 (rounded to the nearest cent).

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To calculate the worth of your investment in 7 years, we need to calculate the future value of the two separate investments and then add them together.