1. **Problem statement:** Calculate the remaining debt (Restschuld) after 5 years for a loan of 2,500,000 with an annual interest rate of 7% and an annuity payment of 274,490. 2. **Formula used:** The remaining debt after $n$ years for an annuity loan is given by: $$\text{Restschuld} = K \cdot (1 + i)^n - R \cdot \frac{(1 + i)^n - 1}{i}$$ where: - $K$ = initial loan amount - $i$ = annual interest rate (decimal) - $n$ = number of years - $R$ = annual annuity payment 3. **Given values:** $$K = 2,500,000$$ $$i = 0.07$$ $$n = 5$$ $$R = 274,490$$ 4. **Calculate $(1 + i)^n$:** $$ (1 + 0.07)^5 = 1.07^5 = 1.402551$$ 5. **Calculate the first term:** $$K \cdot (1 + i)^n = 2,500,000 \times 1.402551 = 3,506,377.5$$ 6. **Calculate the second term denominator:** $$i = 0.07$$ 7. **Calculate the numerator of the second term:** $$ (1 + i)^n - 1 = 1.402551 - 1 = 0.402551$$ 8. **Calculate the fraction:** $$ \frac{0.402551}{0.07} = 5.75073$$ 9. **Calculate the second term:** $$R \times 5.75073 = 274,490 \times 5.75073 = 1,577,956.5$$ 10. **Calculate the remaining debt:** $$\text{Restschuld} = 3,506,377.5 - 1,577,956.5 = 1,928,421$$ **Answer:** The remaining debt after 5 years is approximately **1,928,421**.