Find the total amount in the compound intrest account.
$4000 is compounded annually at a rate of 11% for 3 years. (Round the nearest hundredths as needed)
Sn = P(1+i)^n
Sn = 4000(1.11)^3 = $5,470.52.
To find the total amount in a compound interest account, we can use the formula:
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, $4000)
r = the annual interest rate (in decimal form, 11% is 0.11)
n = the number of times that interest is compounded per year (in this case, compounded annually)
t = the number of years the money is invested for (in this case, 3 years)
Plugging in the given values into the formula, we get:
A = 4000(1 + 0.11/1)^(1*3)
= 4000(1 + 0.11)^3
Now, let's calculate step by step:
1 + 0.11 = 1.11
1.11^3 = 1.36631
A = 4000(1.36631)
= 5465.24
Therefore, the total amount in the compound interest account after 3 years is $5465.24 (rounded to the nearest hundredths).