400 dollor is invested in an account which pays 10% per year compound interest. find the total interest earned if the money is left in the account for 3 years.
To calculate the total interest earned, we need to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment (including the principal and interest)
P = the principal investment amount (initial deposit)
r = annual interest rate (in decimal form)
n = number of times that interest is compounded per year
t = number of years the money is left in the account
In this case:
P = $400
r = 10% = 0.1 (in decimal form)
n = 1 (interest is compounded annually)
t = 3 years
Plugging in these values into the formula:
A = 400(1 + 0.1/1)^(1*3)
A = 400(1.1)^3
A = 400(1.331)
A = 532.4
Therefore, the total amount with interest after 3 years in the account will be $532.4.
To calculate the total interest earned, we subtract the initial amount invested from the final amount:
Total interest = A - P
Total interest = 532.4 - 400
Total interest = $132.4
Thus, the total interest earned after 3 years is $132.4.