Final answer:
The future value of your aunt's bank CD investment after 4 years will be $10,133.79, calculated using the compound interest formula with semi-annual compounding.
Step-by-step explanation:
Calculating the Future Value of a Bank CD
To calculate the future value of your aunt's investment, we can use the formula for compound interest. The formula for compound interest is:
A = P(1 + r/n)ⁿᵗ
where:
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- A is the amount of money accumulated after n years, including interest.
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- P is the principal amount (the initial amount of money).
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- r is the annual interest rate (in decimal).
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- n is the number of times that interest is compounded per year.
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- t is the time the money is invested for in years.
In your aunt's case, the investment details are as follows:
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- Principal (P) = $7,000
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- Annual interest rate (r) = 9.50% or 0.095 (in decimal)
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- Number of times compounded annually (n) = 2 (since it is compounded semi-annually)
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- Time (t) = 4 years
Substituting these values into the compound interest formula gives us:
A = 7000(1 + 0.095/2)²*⁴
Calculating the values within the parentheses and then raising that value to the power of 8, we get:
A = 7000(1.0475)⁸
Now we calculate the value raised to the power of 8:
A = 7000 * 1.447684903
And finally, multiplying this with the principal gives us:
A = $10,133.79 (rounded to two decimal places)
Therefore, after 4 years, your aunt's investment in the bank CD will have grown to $10,133.79.