Suppose you have $\$ 10000$ deposited at $2.55 \%$ compounded quarterly. About long will it take your balance to increase to $\$ 11700$ ? years Round your answer to the nearest tenth of a year

Step 1 ：Given that the principal amount (P) is $10000, the annual interest rate (r) is 2.55%, the number of times that interest is compounded per year (n) is 4, and the final amount (A) is $11700.

Step 2 ：We can use the formula for compound interest, which is A = P(1 + r/n)^(nt), and rearrange it to solve for t: t = log(A/P) / (n * log(1 + r/n)).

Step 3 ：Substitute the given values into the formula: t = log(11700/10000) / (4 * log(1 + 0.0255/4)).

Step 4 ：Solving the equation gives t = 6.2.

Step 5 ：\(\boxed{6.2}\) years is the time it will take for the balance to increase to $11700.