To calculate the final amount of Anne’s investment using the compound interest formula, you can use the following formula:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \(A\) = the amount of money accumulated after n years, including interest.
- \(P\) = principal amount (the initial amount of money).
- \(r\) = annual interest rate (decimal).
- \(n\) = number of times that interest is compounded per unit \(t\).
- \(t\) = the number of years the money is invested or borrowed.
For Anne's investment:
- \(P = 7000\)
- \(r = 3.3% = 0.033\)
- \(n = 4\) (since the interest is compounded quarterly)
- \(t = 25\)
Now plug the values into the formula:
\[ A = 7000 \left(1 + \frac{0.033}{4}\right)^{4 \times 25} \]
Calculating each part step-by-step:
- Calculate \(\frac{0.033}{4}\):
\[ \frac{0.033}{4} = 0.00825 \]
- Calculate \(1 + 0.00825\):
\[ 1 + 0.00825 = 1.00825 \]
-
Calculate \(4 \times 25 = 100\).
-
Raise \(1.00825\) to the power of 100:
\[ 1.00825^{100} \approx 2.246122 \]
- Finally, multiply by the principal amount:
\[ A \approx 7000 \times 2.246122 \approx 15723.86 \]
Thus, Anne’s final amount after 25 years of investment is approximately $15,723.86.
Final answer: Anne's final amount after 25 years of investment is $15,723.86.
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