$300 invested at 9% compounded daily after a period of 4 years.
After 4 years, the investment results in $____.
300(1 + .09/365)^(365*4) = _____
To calculate the value of the investment after 4 years, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
where:
A = the final amount
P = the initial principal amount ($300)
r = the annual interest rate (9%, or 0.09)
n = the number of times interest is compounded per year (365, since it's compounded daily)
t = the number of years (4)
Plugging in the values into the formula:
A = 300(1 + 0.09/365)^(365*4)
Using a calculator, we can compute:
A ≈ 300(1 + 0.0002479)^(1460)
A ≈ 300(1.0002479)^1460
A ≈ 300(1.411581)
A ≈ $423.47
So, after 4 years, the investment would result in approximately $423.47.
To find the final amount of an investment compounded daily, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount
P is the principal amount (the initial investment)
r is the annual interest rate (in decimal form)
n is the number of times interest is compounded per year
t is the number of years
In this case, the principal amount (P) is $300, the annual interest rate (r) is 9% (or 0.09 in decimal form), the number of times interest is compounded per year (n) is 365 (daily compounding), and the number of years (t) is 4.
Plugging in these values into the formula, we have:
A = 300(1 + 0.09/365)^(365*4)
Calculating this expression, we find:
A ≈ $431.12
Therefore, after 4 years, the investment results in approximately $431.12.