How much interest is earned on a principle of $646 invested at a compound interest rate of 5% compounded annually for 10 years?
The formula to calculate compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (in this case, $646)
r = the annual interest rate (5% or 0.05)
n = the number of times that interest is compounded per year (1, since it is compounded annually)
t = the number of years the money is invested for (10 years)
Plugging in the values:
A = 646(1 + 0.05/1)^(1*10)
A = 646(1 + 0.05)^10
A = 646(1.05)^10
A = 646(1.62889531693)
A = $1,053.62
Now, we can calculate the amount of interest earned by subtracting the principal amount from the total amount:
Interest = $1,053.62 - $646
Interest = $407.62
Therefore, the total interest earned on a principal of $646 invested at a compound interest rate of 5% compounded annually for 10 years would be $407.62.