IKT 356
Sample Midterm 1
§ There are 4 questions.
§ Duration is 100 min
§ You must show your work clearly and legibly to receive full credit.
Name:______
Signature:______
Grade (out of 100):______
Problem 1 (10 pts):
Suppose that a father, on the day his son is born, wishes to determine what amount would have to be deposited into an account with an interest of 10% per year to provide withdrawals of 2000 on each of the son’s 18th, 19th, 20th, and 21st birthdays. Draw the cash flow diagram and determine the initial deposit amount.
Problem 2(30 pts): Find the present worth of the cash flows in the following diagram assuming a yearly interest rate of i where i = 10% per year until and including year 18 and i=12% per year thereafter.
Note: Be careful about the timings of the cash flows. 1000$ and 2000$ withdrawals are made in every two years and 3000$ deposits are made in every 4 years.
Problem 3(30 pts): Suppose that you borrow a loan of amount P from a bank at the end of month 3 and make the monthly deposits to the bank as in the cash flow diagram below. In the following cash flow diagram, A7=A8=A9=1000, and starting with A10, the deposits start decreasing in the amount of 40. However, due to a cash problem, you miss a payment at month 12 but continue with your original payment plan thereafter (that is, A10=960, A11=920, A12=0, A13=840 etc.). With these payments, your debt to the bank will be 0 at the end of month 20. Assuming that the interest rate is 12% compounded monthly,
a) Find out the initial loan amount P.
b) Find the total interest paid to the bank
c) Find the interest payment and principal payment components of the payment made in month 13.
Problem 4(30 points)
Consider an investment that requires the purchase of a machine at a price of $10,000. You plan to use this machine for the production of a certain product. The operating costs are expected to be $1000 per month. With this machine, you expect to produce and sell 100 units of a certain product per month at the price of $20 per unit. You also plan to increase the selling price of your product by 10% at the beginning of every year. You plan to continue the production for the next 30 years, however, the life of the machine is expected to be 5 years. Thus, in every 5 years you need to renew the machine. Assume that the cost of the machine increases by $5000 in every 5 years (Thus, the cost of the machine will be $15000 at year 5, $20000 at year 10 etc.). Assuming that the market interest rate is 20% compounded quarterly, write an equation that calculates the net present worth of this investment. Note that you are only required to write the necessary equations, you are not expected to calculate the final result.