1. **Problem Statement:** Calculate the annual amortizing loan payments for two loan proposals and the payment difference when extending the loan term. 2. **Formula for annual amortizing payment:** $$P = \frac{r \times L}{1 - (1 + r)^{-n}}$$ where: - $P$ = annual payment - $r$ = annual interest rate (decimal) - $L$ = loan principal - $n$ = number of years (loan term) 3. **Bank consortium's proposal:** - Principal $L = 220,000,000$ - Interest rate $r = 12.247\% = 0.12247$ - Maturity $n = 4$ years Calculate payment: $$P = \frac{0.12247 \times 220,000,000}{1 - (1 + 0.12247)^{-4}}$$ Calculate denominator: $$1 - (1.12247)^{-4} = 1 - \frac{1}{(1.12247)^4} = 1 - \frac{1}{1.5747} = 1 - 0.6353 = 0.3647$$ Calculate numerator: $$0.12247 \times 220,000,000 = 26,943,400$$ Calculate payment: $$P = \frac{26,943,400}{0.3647} = 73,876,000$$ 4. **Sahara's loan preferences:** - Principal $L = 220,000,000$ - Interest rate $r = 11.746\% = 0.11746$ - Maturity $n = 6$ years Calculate payment: $$P = \frac{0.11746 \times 220,000,000}{1 - (1 + 0.11746)^{-6}}$$ Calculate denominator: $$1 - (1.11746)^{-6} = 1 - \frac{1}{(1.11746)^6} = 1 - \frac{1}{1.898} = 1 - 0.527 = 0.473$$ Calculate numerator: $$0.11746 \times 220,000,000 = 25,841,200$$ Calculate payment: $$P = \frac{25,841,200}{0.473} = 54,615,000$$ 5. **Payment drop if bank consortium loan extended from 4 to 6 years:** Calculate payment for 6 years at 12.247%: $$P_{6yr} = \frac{0.12247 \times 220,000,000}{1 - (1 + 0.12247)^{-6}}$$ Denominator: $$1 - (1.12247)^{-6} = 1 - \frac{1}{(1.12247)^6} = 1 - \frac{1}{2.012} = 1 - 0.497 = 0.503$$ Numerator: $$26,943,400$$ Payment: $$P_{6yr} = \frac{26,943,400}{0.503} = 53,555,000$$ Payment drop: $$73,876,000 - 53,555,000 = 20,321,000$$ **Final answers:** - a. Bank consortium's annual payment (4 years, 12.247%): **73,876,000** - b. Sahara's annual payment (6 years, 11.746%): **54,615,000** - c. Payment drop if bank loan extended from 4 to 6 years: **20,321,000**