If $2500 is invested at an interest rate of 2.5% per year, compouded daily, find the value of the inevestment after 2 years
2500 (1+.025/365)^(365*2) = 2628.17
To find the value of an investment after a certain period of time, 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 (initial investment)
r is the annual interest rate (expressed as a decimal)
n is the number of times that interest is compounded per year
t is the time in years
In this case, the principal amount (P) is $2500, the annual interest rate (r) is 2.5% (0.025 as a decimal), the number of times interest is compounded per year (n) is 365 (since it's compounded daily), and the time (t) is 2 years.
Plugging in these values into the formula, we get:
A = 2500(1 + 0.025/365)^(365*2)
Calculating the result:
A ≈ 2500(1.00006849315)^(730)
A ≈ 2500 * 1.05126717611
A ≈ $2,628.17
Therefore, the value of the investment after 2 years, compounded daily at an interest rate of 2.5%, is approximately $2,628.17.