1. **State the problem:** Eric opened a savings account with 900 on January 2. The bank pays 2% interest per year, compounded quarterly on April 1, July 1, October 1, and January 1. We need to find the amount in the account on the following January 2 and the total interest earned during the year. 2. **Formula and rules:** The interest rate per quarter is $\frac{2\%}{4} = 0.5\% = 0.005$. The formula for compound interest applied quarterly is: $$ A = P \left(1 + r\right)^n $$ where $P$ is the principal, $r$ is the interest rate per quarter, and $n$ is the number of quarters. 3. **Calculate the number of quarters:** From January 2 to the next January 1 is 4 quarters (April 1, July 1, October 1, January 1). 4. **Calculate the amount on January 1:** $$ A = 900 \times (1 + 0.005)^4 $$ 5. **Calculate intermediate steps:** $$ (1 + 0.005)^4 = (1.005)^4 $$ Calculate $ (1.005)^4 $: $$ (1.005)^2 = 1.010025 $$ $$ (1.010025)^2 = 1.020150501 $$ 6. **Calculate final amount:** $$ A = 900 \times 1.020150501 = 918.135451 $$ 7. **Calculate interest earned:** $$ \text{Interest} = A - P = 918.135451 - 900 = 18.135451 $$ 8. **Final answers:** - Amount on January 2 next year: approximately $918.14$ - Interest earned during the year: approximately $18.14$