T. c. hardware store wants to construct a new building at a second location. if construction could begin immediately, the cost would be $500,000. at this time, however, the owners do not have the required 20% down payment, so they plan to invest $2000 per month of their profits until they have the necessary amount. they can invest their money in an annuity account that pays 6%, compounded monthly, but they are concerned about the 3% average inflation rate in the construction industry. they would like you to give them some projections about how 3% inflation will affect the time required to accrue the down payment and the buildingâ€tms eventual cost. they would also like to know how their projected profits, after the new building is complete, will affect their schedule for paying off the mortgage loan. 1. if the 3% annual inflation rate is accurate, how long will it take to get the down payment? (hint: assume that inflation is compounded monthly. then the required down payment will be 20% of (500,000(1+(0.03/12))^n. where n is in months. 2. if the 3% annual inflation rate is accurate (compounded monthly), what will t. c. hardware's projected construction costs be when it has the down payment? 3. if t. c. hardware borrows 80% of its construction costs and amortizes that amount at 7.8% monthly for 15 years, what will the monthly payment be? 4. after 2 years, the profits will increase enough so they can make double mortgage payments each month until loan gets paid. how long will it take t. c. hardware to pay off the loan?