ISyE3025_Spring09_HW1_Soln - ISyE 3025, Spring09 , HW1,...

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1 of 5 ISyE 3025, Spring09 , HW1, Solutions This homework is intended for Learning Cycle 1, leading to Exam 1 1. In 1948 your grandfather left your mother a $5,000 U.S. government bond, to be used for your education. The annual interest rate was 1.9%. The annual interest was left to accumulate with the bond according to compound interest. Then your mother redeemed (cashed in) the bond. What were the cash proceeds many years later, in 2004? Solution: Answer uses F/P factor. F 0 i per year N P F = $5,000 (F/P, 1.9%, 2004-1948) = 5,000(1 + .019)^56 = $14,346. 2. You wish to join a club that has an initiation fee of $40,000. You only have $23,000 available for this right now. You can invest in a fund that pays 3.5% per year. If you invest your money in this fund, how many years must you wait until it will grow to the required amount for the initiation fee? [Assume the initiation fee does not change, due to inflation or other reasons] Solution : Answer involves manipulation of F/P factor. $40,000 = $23,000 (F/P, 3.5%, N) = 23,000(1 + .035)^N 40,000/23,000 = 1.035^N N = ln(40/23)/ln(1.035) = 0.5534/0.0344 = 16.09, round up to 17 because interest is paid at the end of the year on this account. It will take 17 years to accumulate. [Can also solve by trial-and-error.] [Diagram is similar to previous one.] 3. A certain investment is available that promises to return $7,000 five years from now. If the investor's "time value of money" is 4.5% per year, find the equivalent present value of this proposed investment. Solution : Answer uses P/F factor. P = $7,000 (P/F, 4.5%, 5) = 7,000(1.045)^(-5) = $5,617. [Diagram is similar to previous one.] 4. You expect to receive a future amount at the end of year 200Y. However, you wish instead to receive this amount earlier, at the end of year 200X, with years shown in the table. At the annual interest rate shown in the table, what is the equivalent amount at the end of Year 200X? Future amount Year 200Y Annual interest rate Year 200X $ 2,000 2008 6% 2005 Solution : Answer uses P/F factors. Take year 2005 as reference point. P = $2,000 (P/F, 6%, 2008-2005) = $2,000(1.06)^-3 = $1,679. 5. You are presented with two investment opportunities, A and B as described below. A choice of either one would require the initial investment now (if you select either investment opportunity, you cannot invest less or more in that opportunity, only the amount shown). In addition, you can always invest in a fund that pays 5% per year. You currently have $4,000 to invest. If you wish to maximize your cash amount at the end of year 6, which of the two investments, A or B, is the better choice? You cannot select both. Explain numerically. Investment opportunity A B Initial investment needed $4,000 $3,200 Annual interest rate 7% 9% Length of investment 6 years 5 years Solution : Answer requires use of F/P factor, selection of a common horizon time , and consideration of unused funds , which would be invested at 5%.
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This note was uploaded on 09/07/2009 for the course ISYE 3025 taught by Professor Lee during the Spring '09 term at Georgia Institute of Technology.

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ISyE3025_Spring09_HW1_Soln - ISyE 3025, Spring09 , HW1,...

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