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.)
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To calculate the worth of your investment in 7 years, let's break down the calculations for each investment option:
1. Gold investment:
- The value of gold is growing by 12% per year.
- To calculate the value after 7 years, multiply the initial investment by (1 + growth rate) raised to the power of the number of years: $5,000 * (1 + 0.12)^7.
2. CD investment:
- The CD interest rate is 5% per year, compounded semi-annually.
- To calculate the value after 7 years, we need to compound the interest semi-annually.
- The interest rate per period is (5 / 2)% = 2.5%.
- The number of compounding periods in 7 years is 7 * 2 = 14.
- To calculate the value after 7 years, multiply the initial investment by (1 + interest rate per period) raised to the power of the number of compounding periods: $5,000 * (1 + 0.025)^14.
Now let's calculate the values for each investment:
1. Gold investment:
$5,000 * (1 + 0.12)^7 = $5,000 * 1.967151 = $9,835.76
2. CD investment:
$5,000 * (1 + 0.025)^14 = $5,000 * 1.388886 = $6,944.43
Finally, to calculate the total worth of your investment in 7 years, add the values of the two investments:
$9,835.76 + $6,944.43 = $16,780.19
Therefore, your investment will be worth approximately $16,780.19 in 7 years.