To calculate the balance of an investment compounded annually, you can use the formula for compound interest:
\[ A = P(1 + r)^t \]
where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (decimal).
- \( t \) is the number of years the money is invested or borrowed.
Given:
- \( P = 20000 \)
- \( r = 0.05 \) (5% as a decimal)
- \( t = 5 \)
Now plug in the values into the formula:
\[ A = 20000(1 + 0.05)^5 \]
Calculating inside the parentheses first:
\[ A = 20000(1.05)^5 \]
Now calculate \( (1.05)^5 \):
\[ (1.05)^5 \approx 1.2762815625 \]
Now multiply by the principal:
\[ A \approx 20000 \times 1.2762815625 \approx 25525.63 \]
Thus, the balance after 5 years will be approximately $25,525.63.
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