# Question #1 Rates are 8% p.a. compounded semi-annually

Question #1 Rates are 8% p.a. compounded semi-annually. a. What is the value today of a security that promises to pay you \$10,000 each two years forever with the first cash flow due in exactly1 year? b. What is the value today of a security that promises to pay you \$10,000 each two years with the first cash flow due today?

Question #2 Rates are 8% p.a. compounded semi-annually. a. You are going to make 30 monthly deposits of \$500 each into your bank account starting in exactly 1 month. How much will you have immediately after the last deposit? b. You are going to make 30 monthly deposits of \$500 each into your bank account starting in exactly 7 months. How much will you have immediately after the last deposit? c. You made the first of 30 monthly deposits of \$500 each into your bank account exactly 7 months ago. How much will you have immediately after the last deposit?

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Question #3 a. Rates are currently 7% p.a. You wish to purchase a security that pays out \$500 each 3 months starting in exactly 2 month’s time. The security will pay out a total of 30 payments. What is the fair purchase price of the security? b. Assume that you purchased the above security. Imagine that exactly 1 year has passed. You now wish to sell the security. However, interest rates have now fallen to 6% p.a. compounded monthly. What is the fair selling price of the security?

Question #4 You own a house on a plot of land. The land has a value of \$150,000. Use of the house has a value to you. You believe that the first years benefit to you amounts to \$8000. Assume that this is as though you get \$8000 at the end of the first year. Thereafter the annual benefits diminish at 4% per year. Furthermore, assume that the house will have to be demolished in exactly 22 years. Assume that rates are 8% p.a. Assume the land value remains unchanged over time. a. What is the total value of the house and land? b. You enter into a contract to sell the house. The purchaser will take possession in exactly 6 years. The purchaser uses the same method of valuation as you have. However, you want payment today. What amount will the purchaser be willing to give you today?

Question #5 Exactly 5 years ago, Y made the first of several semi-annual deposits in the bank earning interest at the rate of 8% p.a. effective. Each of these deposits was \$1,000. The last deposit occurred a few minutes ago. This bank account will fund a series of withdrawals. These will occur annually with the first in exactly 1 year. There will be a total of 12 withdrawals. Each of the first 6 will be for the same amount. Each of the remaining 6 will be exactly twice the amount of each of the first 6. (E.g. if the first 6 are for \$1,000 each then each of the remaining 6 will be \$2,000). If interest rates are now changing to 8% p.a. compounded semi-annually, what are the magnitudes of the withdrawals?

Question #6 Z wants to plan for the future by investing on a regular basis. The investment plan needs to provide for his retirement and the university education of his small child. His child’s university education will require a series of 4 annual withdrawals starting in exactly 16 years. Each withdrawal would have the same purchasing power as \$15000 today. Inflation is expected to be 2.5% p.a. indefinitely. When he retires, Z will make annual withdrawals starting in exactly 41 years. Each withdrawal will be \$50000. He plans to make a total of 20 withdrawals. He intends making annual payments starting today. He intends making his last deposit in exactly 40 years. Interest rates are, and are expected to remain at 6% p.a. compounded monthly. The bank manager will permit Z to go into overdraft if he needs to. The overdraft rate will also be 6% p.a. compounded monthly. a. How much must Z deposit annually to achieve his plan? b. What will his bank balance be immediately after he has made the 4th withdrawal for his child’s education?

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