To calculate the amount in the account after 10 years, we can use the formula for compound interest:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
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).
- \(n\) is the number of times that interest is compounded per year.
- \(t\) is the number of years the money is invested or borrowed.
Given:
- \(P = 5619\)
- \(r = 4.04% = 0.0404\) (as a decimal)
- \(n = 4\) (quarterly compounding)
- \(t = 10\)
Now we can plug these values into the formula:
\[ A = 5619 \left(1 + \frac{0.0404}{4}\right)^{4 \times 10} \]
Calculating \(\frac{0.0404}{4}\):
\[ \frac{0.0404}{4} = 0.0101 \]
Now plug this into the formula:
\[ A = 5619 \left(1 + 0.0101\right)^{40} \]
This becomes:
\[ A = 5619 (1.0101)^{40} \]
Now we need to calculate \((1.0101)^{40}\):
\[ (1.0101)^{40} \approx 1.488864 \]
Now multiply this by the principal:
\[ A \approx 5619 \times 1.488864 \approx 8366.40 \]
Rounding to the nearest dollar:
\[ A \approx 8366 \]
Thus, the amount in the account after 10 years will be approximately $8,366.
1 answer