Calculate the final value after 10 years if you invest $5000.00 at 2.5% per annum, compounded annually.
1.025^10 = 1.280084544
* 5000 = 6400.42
To calculate the final value after 10 years if you invest $5000.00 at 2.5% per annum, compounded annually, we can use the formula for compound interest:
F = P(1 + r/n)^(nt)
Where:
F = the future value or the final value
P = the principal amount (initial investment)
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years
In this case:
P = $5000.00
r = 2.5% or 0.025 (converted to decimal form)
n = 1 (compounded annually)
t = 10 years
Plugging in the values into the formula, we have:
F = 5000(1 + 0.025/1)^(1*10)
Simplifying further:
F = 5000(1 + 0.025)^10
Using a calculator or a math software, we can compute:
F ≈ 5000(1.025)^10
F ≈ 5000(1.2800845)
F ≈ $6400.42
Therefore, the final value after 10 years would be approximately $6400.42.