HW1_Solutions.pdf - IE 4850 Engineering Economy Homework 1...

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1 IE 4850 Engineering Economy Homework 1 1. (7 mins) A bank offers you a nominal interest of 6% per year compounding quarterly on your savings. o What is the effective interest rate per quarter? o What is the effective interest rate per year? o What is the effective interest rate per two years? a) ࠵?/࠵? = ࠵?. ࠵?% b) (࠵? + ࠵?. ࠵?࠵?࠵?) ࠵? c) (࠵? + ࠵?. ࠵?࠵?࠵?) ࠵? 2. (5 mins) In 1962 your grandfather left your mother $5,000, to be used for your education. The annual interest rate was 1.9%. Then your mother redeemed (cashed in) the bond in 2018. What were the value of money many years later, in 2018? = ࠵?࠵?࠵?࠵? ∗ ࠵?. ࠵?࠵?࠵? ࠵?࠵?࠵?࠵?ି࠵?࠵?࠵?࠵? = ࠵?࠵?࠵?࠵? ∗ ࠵?. ࠵?࠵?࠵? ࠵?࠵?
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2 3. (5 mins) A certain investment is available that promises to return $7,000 five years from now. If the interest rate is 4.5% per year, find the equivalent present value of this proposed investment. = ࠵?࠵?࠵?࠵? ࠵?.࠵?࠵?࠵? ࠵? 4. (15 mins) How much must be invested today in order to provide annual benefits of $40,000 per year for 30 years, with the first payment occurring exactly 42 years from now, if the interest rate is 3.5% per year? Table for 3.5% interest rate is not provided, thus you need to use the formula at the penultimate page.
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3 5. (15 mins) Consider the sequence of cash flows given in the table. Find the net present value (NPV) of the cash flow. Interest rate is 20%. End of Period 0 1 2 3 4 5 6 ... 14 15 Cash Flow 0 500 550 600 650 700 750 ... 1150 1200 = 500 (P|A,i = 20%, n = 15)+ 50 (P|G,i = 20%, n = 15) 6. (NG: 20 mins) [DIFFICULT] Consider the sequence of cash flows given in the table. Find the net present value (NPV) of the cash flow. Interest rate is 20%. End of Period 0 1 2 3 4 5 6 ... 14 15 Cash Flow 1600 1500 1400 1300 1200 1100 1000 ... 200 100 = 1500 (P|A,i = 20%, n = 15)- 100 (P|G,i = 20%, n = 15) + 1600 (note that period zero has positive cash)
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4 7. (10 mins) A project requires an investment of purchase for equipment. The salvage value of the equipment at the end of the project life is the salvage. In addition, annual expenses for operation and maintenance are denoted by O&M. With interest rate = 20%, find the net present value of this project. Pay attention to the signs of the cash flows: + for inflows, - for outflows.
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