$400 invested at 3% compounded daily after a period of 3 years=$?(round to nearest cent)
i = .03/365 = .000082191
n = 3(365) = 1095
amount = 400(1.000082191)^1095 = 437.67
(using continuous compounding it would be
400 e^(3(.03)) = 400 e^.09 = 437.67 )
To calculate the future value of an investment compounded daily, you can use the formula:
\[ A = P(1 + \frac{r}{n})^{nt} \]
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate (expressed as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case, we have:
P = $400
r = 3% = 0.03 (since 3% is equivalent to 0.03 as a decimal)
n = 365 (since interest is compounded daily)
t = 3 years
Plugging these values into the formula, we get:
\[ A = 400(1 + \frac{0.03}{365})^{365 \times 3} \]
Now let's calculate this value:
\[ A = 400(1 + \frac{0.03}{365})^{1095} \]
Calculating \((1 + \frac{0.03}{365})^{1095}\) gives us approximately 1.093451.
\[ A = 400 \times 1.093451 \approx 437.38 \]
Therefore, after a period of 3 years, $400 invested at 3% compounded daily would amount to approximately $437.38 (rounded to the nearest cent).