1. Perform the required calculations using time value of money principles and show your work to the extent reasonably possible. For example, when using Excel, use separate cells for inputs instead of embedding all numbers in a formula. 2. Solve each of the following problems: 2.1. You are considering purchasing a house that costs $285,000. You must make a down payment of 15% of the value of the house. Four percent of the purchase price less the down payment will be added to the total amount borrowed in order to cover the closing costs. The total loan balance may be borrowed over 30 years at 7% interest. Calculate the monthly payment for the mortgage. 2.2. Create the first three periods of the amortization table for the mortgage in the prior problem. 2.3. You believe that you can pay $400 per month in addition to the payment calculated in problem 2.1. No penalty is charged for early payment. How long will it take you to pay off the mortgage under these circumstances? 2.4. You have decided to sell the house at the end of 10.5 years (126 payments). Using the information from problems 2.1 and 2.2, how much do you still owe on the mortgage when you sell the home? 2.5. A company invests $6 million dollars to purchase and update the landscaping on a piece of real estate. As the trees and shrubs mature, the building site is expected to increase in value due to the more attractive nature of the landscaping and the panoramic views of a nearby city. The site is expected to sell for $15 million dollars eight years from now. What is the company's expected nominal annual rate of return on this real estate investment? 2.6. Suppose you have $1,000 invested in an investment yielding a continuously compounded nominal rate of 4.75% per year. How much money would you have after 9.25 years? 2.7. Find the effective rates for each of the following investments, and then determine which of the investments would you prefer to invest in (assume the risk is the same for all three investments): Investment A: An investment offering 10% simple interest per year Investment B: An investment offering 9.75% nominal interest per year compounded quarterly Investment C: An investment offering 9.50% nominal interest per year compounded continuously 2.8. A reputable individual approaches you for a loan. He wishes to borrow $845 from you today. In exchange, he will give you $21 at the end of every three months and $1085 at the end of 7 years. Assuming you have the money to lend to him, what would be your overall annual rate of return on this loan if you lend him the money? 2.9. Assume that today is January 1, 2023. A client of your financial advisement firm is creating a plan to meet his financial goals. First, he would like to retire twenty years from now when he is fifty-five years old (first retirement payment January 1, 2043). He wants an annual retirement income of $87,000 per year for forty years. Second, he would like to purchase a used sports car Page 1 of 2 Time Value of Money Fall 2022 eight years from now, with an estimated cost of $66,000. He can afford to save only $9,750 per year for the first ten years. He expects to earn 7% per year on average from investments over his lifetime. What must his minimum annual savings be in order for him to meet his objectives, beginning after the first ten years and lasting until he retires? For the sake of simplicity, assume that he makes savings payments at the end of each year. 2.10. How much do you have to save at the end of every month for only 15 years to have a perpetuity of $76,000, assuming that you can invest an at annual rate of 9% ? Assume that the first deposit is at the end of the first month, and that the first payment will be at the beginning of the twenty-fifth year. 1. Perform the required calculations using time value of money principles and show your work to the extent reasonably possible. For example, when using Excel, use separate cells for inputs instead of embedding all numbers in a formula. 2. Solve each of the following problems: 2.1. You are considering purchasing a house that costs $285,000. You must make a down payment of 15% of the value of the house. Four percent of the purchase price less the down payment will be added to the total amount borrowed in order to cover the closing costs. The total loan balance may be borrowed over 30 years at 7% interest. Calculate the monthly payment for the mortgage. 2.2. Create the first three periods of the amortization table for the mortgage in the prior problem. 2.3. You believe that you can pay $400 per month in addition to the payment calculated in problem 2.1. No penalty is charged for early payment. How long will it take you to pay off the mortgage under these circumstances? 2.4. You have decided to sell the house at the end of 10.5 years (126 payments). Using the information from problems 2.1 and 2.2, how much do you still owe on the mortgage when you sell the home? 2.5. A company invests $6 million dollars to purchase and update the landscaping on a piece of real estate. As the trees and shrubs mature, the building site is expected to increase in value due to the more attractive nature of the landscaping and the panoramic views of a nearby city. The site is expected to sell for $15 million dollars eight years from now. What is the company's expected nominal annual rate of return on this real estate investment? 2.6. Suppose you have $1,000 invested in an investment yielding a continuously compounded nominal rate of 4.75% per year. How much money would you have after 9.25 years? 2.7. Find the effective rates for each of the following investments, and then determine which of the investments would you prefer to invest in (assume the risk is the same for all three investments): Investment A: An investment offering 10% simple interest per year Investment B: An investment offering 9.75% nominal interest per year compounded quarterly Investment C: An investment offering 9.50% nominal interest per year compounded continuously 2.8. A reputable individual approaches you for a loan. He wishes to borrow $845 from you today. In exchange, he will give you $21 at the end of every three months and $1085 at the end of 7 years. Assuming you have the money to lend to him, what would be your overall annual rate of return on this loan if you lend him the money? 2.9. Assume that today is January 1, 2023. A client of your financial advisement firm is creating a plan to meet his financial goals. First, he would like to retire twenty years from now when he is fifty-five years old (first retirement payment January 1, 2043). He wants an annual retirement income of $87,000 per year for forty years. Second, he would like to purchase a used sports car Page 1 of 2 Time Value of Money Fall 2022 eight years from now, with an estimated cost of $66,000. He can afford to save only $9,750 per year for the first ten years. He expects to earn 7% per year on average from investments over his lifetime. What must his minimum annual savings be in order for him to meet his objectives, beginning after the first ten years and lasting until he retires? For the sake of simplicity, assume that he makes savings payments at the end of each year. 2.10. How much do you have to save at the end of every month for only 15 years to have a perpetuity of $76,000, assuming that you can invest an at annual rate of 9% ? Assume that the first deposit is at the end of the first month, and that the first payment will be at the beginning of the twenty-fifth year