To calculate the total amount due after 5 years on a principal amount of $6,635.73 at an annual interest rate of 7.5%, with interest accruing daily, we can use the formula for compound interest. The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \(A\) = the future value of the investment/loan, including interest
- \(P\) = the principal investment amount (the initial deposit or loan amount)
- \(r\) = 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
In this case:
- \(P = 6635.73\)
- \(r = 7.5% = 0.075\)
- \(n = 365\) (interest is compounded daily)
- \(t = 5\)
Let's plug in the values:
\[ A = 6635.73 \left(1 + \frac{0.075}{365}\right)^{365 \times 5} \]
Calculating it step-by-step:
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Calculate \(\frac{r}{n}\): \[ \frac{0.075}{365} \approx 0.00020547945 \]
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Calculate \(nt\): \[ 365 \times 5 = 1825 \]
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Compute \(\left(1 + \frac{r}{n}\right)^{nt}\): \[ A = 6635.73 \left(1 + 0.00020547945\right)^{1825} \] \[ A = 6635.73 \times (1.00020547945)^{1825} \]
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Use a calculator for \((1.00020547945)^{1825}\): \[ A \approx 6635.73 \times 1.478347 \]
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Finally, calculate \(A\): \[ A \approx 9800.66 \]
Thus, the total amount due after 5 years would be approximately $9,800.66.
3 answers