Jackson and Olivia deposited $9,047.00 into a savings account which earns interest compounded monthly. After 8 months, they had $9,779.00 in the account which they used to go on a trip. What was the interest rate on the account?

Round your answer to the nearest tenth of a percent.

11.7%

Step-by-step explanation:

The account balance (A) for a principal amount P and monthly interest rate r will be ...

A = P (1 + r) ^8

Then we can divide by P and take the 8th root to find r:

A/P = (1+r) ^8

(A/P) ^ (1/8) = 1 + r

(A/P) ^ (1/8) - 1 = r

Since this is the monthly rate, we need to multiply this value by 12 to find the annual interest rate on the account:

annual rate = 12 ((A/P) ^ (1/8) - 1) = 12 ((9779/9047) ^ (1/8) - 1) ≈ 0.11728 ≈ 11.7%