1. **State the problem:** We need to find the mortgage balance after the first three payments on a 15-year mortgage of 170000 financed at an APR of 3.5% with monthly payments of 1215.30. 2. **Given data:** - Loan amount (principal) $P = 170000$ - Annual interest rate $r = 3.5\% = 0.035$ - Monthly interest rate $i = \frac{0.035}{12} = 0.0029167$ - Monthly payment $M = 1215.30$ 3. **Formula for mortgage balance after payment $k$:** $$\text{Balance}_k = P(1+i)^k - M \frac{(1+i)^k - 1}{i}$$ 4. **Calculate Balance after 1st payment:** $$\text{Balance}_1 = 170000(1+0.0029167)^1 - 1215.30 \frac{(1+0.0029167)^1 - 1}{0.0029167}$$ Calculate powers and fractions: $$= 170000 \times 1.0029167 - 1215.30 \times \frac{0.0029167}{0.0029167}$$ $$= 170495.83 - 1215.30 = 169280.53$$ 5. **Calculate Balance after 2nd payment:** $$\text{Balance}_2 = 170000(1.0029167)^2 - 1215.30 \frac{(1.0029167)^2 - 1}{0.0029167}$$ Calculate powers: $$= 170000 \times 1.005837 - 1215.30 \times \frac{0.005837}{0.0029167}$$ $$= 171000.29 - 1215.30 \times 2 = 171000.29 - 2430.60 = 168569.69$$ 6. **Calculate Balance after 3rd payment:** $$\text{Balance}_3 = 170000(1.0029167)^3 - 1215.30 \frac{(1.0029167)^3 - 1}{0.0029167}$$ Calculate powers: $$= 170000 \times 1.008763 - 1215.30 \times \frac{0.008763}{0.0029167}$$ $$= 171488.71 - 1215.30 \times 3 = 171488.71 - 3645.90 = 167842.81$$ 7. **Verify with given interest and principal payments:** - After 1st payment: Balance = $170000 - 719.47 = 169280.53$ - After 2nd payment: Balance = $169280.53 - 721.57 = 168558.96$ (close to calculated 168569.69) - After 3rd payment: Balance = $168558.96 - 723.67 = 167835.29$ (close to calculated 167842.81) **Final answers:** - Balance 1: $169280.53$ - Balance 2: $168569.69$ - Balance 3: $167842.81$