When discussing compounding interest that occurs on a weekly basis, it typically refers to how interest on a principal amount is calculated and added to the account balance once every week. Compounding interest more frequently generally results in a higher amount of interest earned compared to monthly or yearly compounding.
Formula for Compound Interest
The formula for calculating compound interest is:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) = the amount of money accumulated after n years, including interest.
- \( P \) = the principal amount (the initial money).
- \( r \) = the annual interest rate (decimal).
- \( n \) = the number of times that interest is compounded per year.
- \( t \) = the number of years the money is invested or borrowed.
For Weekly Compounding
If interest is compounded weekly:
- \( n = 52 \) (since there are 52 weeks in a year)
Example Calculation
Suppose you have:
- \( P = 1000 \) (the initial investment)
- \( r = 0.05 \) (the annual interest rate of 5%)
- \( t = 2 \) years
Plugging these values into the formula:
\[ A = 1000 \left(1 + \frac{0.05}{52}\right)^{52 \times 2} \]
Calculating this step by step:
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Calculate \( \frac{0.05}{52} \): \[ \frac{0.05}{52} \approx 0.00096153846 \]
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Calculate \( 52 \times 2 = 104 \) (the total number of compounding periods).
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Now plug these into the formula: \[ A \approx 1000 \left(1 + 0.00096153846\right)^{104} \] \[ A \approx 1000 \left(1.00096153846\right)^{104} \] \[ A \approx 1000 \times 1.221386025 (approximately) \] \[ A \approx 1221.39 \]
Thus, after 2 years, with weekly compounding at an annual interest rate of 5%, the amount accumulated would be approximately $1221.39.
Summary
Compounding weekly can significantly increase the total amount accrued over time, depending on the interest rate and the duration. If you have more specific parameters or values, feel free to share, and I can help you with the calculation!
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