Question

$6635.73 At 7.5% interest annually, interest will accrue daily until paid in full times 5 years

Answer 1

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:

1. Calculate \(\frac{r}{n}\):
\[
\frac{0.075}{365} \approx 0.00020547945
\]

2. Calculate \(nt\):
\[
365 \times 5 = 1825
\]

3. Compute \(\left(1 + \frac{r}{n}\right)^{nt}\):
\[
A = 6635.73 \left(1 + 0.00020547945\right)^{1825}
\]
\[
A = 6635.73 \times (1.00020547945)^{1825}
\]

4. Use a calculator for \((1.00020547945)^{1825}\):
\[
A \approx 6635.73 \times 1.478347
\]

5. Finally, calculate \(A\):
\[
A \approx 9800.66
\]

Thus, the total amount due after 5 years would be approximately **$9,800.66**.