1. **Problem statement:** Calculate the difference in total interest payable between two loans. 2. **Given:** - Loan 1: Principal £750,000, interest rate 7.8%, total interest £58,500 over 8 years. - Loan 2: Principal £750,000, interest rate 8.1%, term 8 years. 3. **Calculate total interest for Loan 2:** Since interest is proportional to rate for the same principal and time, $$\text{Interest}_2 = \frac{8.1}{7.8} \times 58,500 = 1.03846 \times 58,500 = 60,730.77$$ 4. **Calculate difference in interest:** $$\text{Difference} = 60,730.77 - 58,500 = 2,230.77$$ --- 5. **Problem statement:** Calculate total interest payable at 8.1% interest rate. 6. **Formula:** Interest is proportional to rate, so $$\text{Interest} = \frac{8.1}{7.8} \times 58,500 = 60,730.77$$ --- 7. **Problem statement:** Calculate percentage increase in interest due to rate rise. 8. **Formula:** $$\text{Percentage increase} = \frac{\text{New Interest} - \text{Old Interest}}{\text{Old Interest}} \times 100$$ 9. **Calculation:** $$\frac{60,730.77 - 58,500}{58,500} \times 100 = \frac{2,230.77}{58,500} \times 100 = 3.81\%$$ --- 10. **Problem statement:** Calculate monthly repayment for £90,500 loan over 5 years at 9.8% simple interest. 11. **Calculate total interest:** $$\text{Interest} = 90,500 \times 0.098 \times 5 = 44,345$$ 12. **Calculate total repayment:** $$90,500 + 44,345 = 134,845$$ 13. **Calculate monthly repayment:** $$\frac{134,845}{5 \times 12} = \frac{134,845}{60} = 2,247.42$$ **Final answers:** - Difference in interest between loans: £2,230.77 - Total interest at 8.1%: £60,730.77 - Percentage increase in interest: 3.81% - Monthly repayment for £90,500 loan: £2,247.42