1. **State the problem:** A group of investors bought a condominium for 5 million. They paid 15% down and financed the rest with a loan amortized over 13 years at 5.1% annual interest compounded quarterly. We need to find the quarterly payment $R$. 2. **Identify the loan amount:** The down payment is 15% of 5 million, so the loan amount is 85% of 5 million. $$\text{Loan amount} = 5,000,000 \times (1 - 0.15) = 5,000,000 \times 0.85 = 4,250,000$$ 3. **Formula for amortized loan payment:** The formula for the periodic payment $R$ is $$R = P \times \frac{i}{1 - (1 + i)^{-n}}$$ where: - $P$ is the principal (loan amount), - $i$ is the interest rate per period, - $n$ is the total number of payments. 4. **Calculate $i$ and $n$:** - Annual interest rate is 5.1%, compounded quarterly, so quarterly interest rate is $$i = \frac{5.1\%}{4} = \frac{0.051}{4} = 0.01275$$ - Number of quarters in 13 years: $$n = 13 \times 4 = 52$$ 5. **Substitute values into the formula:** $$R = 4,250,000 \times \frac{0.01275}{1 - (1 + 0.01275)^{-52}}$$ 6. **Calculate the denominator:** $$1 + 0.01275 = 1.01275$$ $$1.01275^{-52} = \frac{1}{1.01275^{52}}$$ Calculate $1.01275^{52}$: $$1.01275^{52} \approx 1.8194$$ So, $$1.01275^{-52} \approx \frac{1}{1.8194} = 0.5499$$ 7. **Calculate denominator:** $$1 - 0.5499 = 0.4501$$ 8. **Calculate fraction:** $$\frac{0.01275}{0.4501} \approx 0.02833$$ 9. **Calculate payment $R$:** $$R = 4,250,000 \times 0.02833 = 120,402.5$$ 10. **Round to nearest cent:** $$R \approx 120,402.50$$ **Final answer:** The required quarterly payment is approximately **120,402.50**. **Note:** The formula used is the amortization payment formula for loans with compound interest.