If $570 is invested in an account that earns 12.75%, copounded annually, what will the account balance be after 11 years?( round to the neearest cent)
To calculate the account balance after 11 years, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Accoount balance
P = Initial amount invested
r = Annual interest rate (as a decimal)
n = Number of times the interest is compounded per year
t = Number of years
In this case:
P = $570 (Initial amount invested)
r = 12.75% = 0.1275 (Annual interest rate expressed as a decimal)
n = 1 (Compounded annually)
t = 11 years
Let's plug in the values into the formula and calculate:
A = 570(1 + 0.1275/1)^(1*11)
First, divide the annual interest rate by the number of times compounded, in this case, r/n:
A = 570(1 + 0.1275)^(11)
Next, raise that sum to the power of (n*t):
A = 570(1.1275)^11
Now, calculate the value inside the parentheses:
A = 570(1.952271726)
Multiply the result by the initial amount invested:
A = 570 * 1.952271726
Finally, calculate the account balance after 11 years:
A = $1,112.29 (rounded to the nearest cent)
Therefore, the account balance will be approximately $1,112.29 after 11 years.