Answer: $2,614.16
Explanation:
Initially, he has $1077.
We know that this has a fixed annual interest rate of 9% compounded three times per year.
(remember that 9% is 0.09 in decimal form)
Then in one year, this interest is compounded in 3 times.
So we actually apply 0.09/3 3 times.
So if in year zero, Ted has $1077.
after 1 year, Ted will have:
M = $1077*(1 + 0.09/3)^3
Where the power of 3 is because this interest rate is applied 3 times.
Now, after another year Ted will have:
M = $1077*(1 + 0.09/3)^3*(1 + 0.09/3)^3 = $1077*(1 + 0.09/3)^(2*3)
We already can see the pattern here, after N years,
M(N) = $1077*(1 + 0.09/3)^(3*N)
The account balance after 10 years can be computed by evaluating the above equation in N = 10.
M(10) = $1077*(1 + 0.09/3)^(3*10) = $2,614.16