1. **State the problem:** Parker has a student loan balance of $26000 with a 4.5% compound interest rate. He defers the loan for one year, and we need to find the additional interest added due to this deferment. 2. **Formula used:** Compound interest is calculated by the formula: $$A = P(1 + r)^t$$ where $A$ is the amount after time $t$, $P$ is the principal, $r$ is the interest rate per period, and $t$ is the number of periods. 3. **Calculate the amount after one year with deferment:** $$A = 26000(1 + 0.045)^1 = 26000 \times 1.045 = 27170$$ 4. **Calculate the interest added due to deferment:** The additional interest is the difference between the amount after one year and the original principal: $$\text{Interest} = A - P = 27170 - 26000 = 1170$$ 5. **Explanation:** The deferment causes the loan balance to grow by $1170$ due to compound interest at 4.5% for one year. **Final answer:** The additional interest added because of the deferment is $1170$.