# Professor Kim wants to open a new Korean restaurant at Latham. A business consultant approximated the cost of construction, interior design, necessary initial procurement of raw materials and equipment, and advertisement as $300,000, if the project begins immediately. After the discussion with the consultant and a Chase Bank, Kim was able to get the preapproval of the loan with the required 20% down payment. At this time, however, Kim do not have the required down payment $60,000 (20% of $300,000). The consultant suggests investing $1000 per month in an annuity account that pays 3% compounded monthly until Kim has the necessary amount. Kim also noticed that there is an inflation of 1.2% across the industry, which implies that the cost of $300,000 will increase when Kim has the down payment from the annuity. Following questions would be helpful to help Kim and give him an idea. Prepare for the financial report to help Kim. (Assume that inflation rate of 1.2% is accurate and compounded monthly.) 1. Write a formula for the value of required down payment ($60,000) after months. 2. Write a formula for a future value of annuity that Kim originated to have the down payment after months. 3. How long will it take to get the down payment? 4. When Kim has the required down payment, what will be the projected construction cost? Round to the nearest cent. 5. The loan manager of Chase Bank projected the interest rates of 2.9%, 3.3%, and 3.8% for different loan periods of 15, 20, and 30 years, respectively. If Kim borrows 80% of the total cost and amortizes the amount, what will be the monthly payment for three options? Write formulas for all options and find the payments.