Atlantic Metals and Plastic uses austenitic nickel-chromiumalloys to manufacture

Question

Atlantic Metals and Plastic uses austenitic nickel-chromiumalloys to manufacture resistance heating wire. The company isconsidering a new annealing-drawing process to reduce costs. If the new process will cost $1.8 million now, how much must besaved each year to recover the investment in 6 years at an interestrate of 12% per year? any help would be great, will rate lifesaver even if you justset up the solution Atlantic Metals and Plastic uses austenitic nickel-chromiumalloys to manufacture resistance heating wire. The company isconsidering a new annealing-drawing process to reduce costs. If the new process will cost $1.8 million now, how much must besaved each year to recover the investment in 6 years at an interestrate of 12% per year? any help would be great, will rate lifesaver even if you justset up the solution

Explanation / Answer

We can view the "recovering of investment" as paying theinvested money, in this case the 1.8 million. The problem specifies6 payments, one made in one year, the second in two years, andso on. In this scenario, the money grows with time because ofthe interest rate 12 % annual, so if I wanted to pay $10000 inone year, I need to have NOW only 10000/( 1.12)=$8928.57, for in one year it will become $10000 because of theinterest.   The $10000 is called the future value, and the$8928.57 is called the present value. The objective of the problem is that the sum of the presentvalues of the 6 payments have to be 1.8 million. The future valueP is unknown. This can be stated in an equation 1 800 000 = P (1 +0.12) -1 + P (1 +0.12)-2 + P (1 +0.12) -3+ P (1 +0.12)-4+P (1 +0.12) -5+ P (1 +0.12)-6 From this P = 1800000 / 4.11140 = $437 806.2931 must be savedeach year Note: A formula to obtain a present value: Vpresent = Vfuture ( 1 + i)-n    i : anual interest rate n: number of years From this P = 1800000 / 4.11140 = $437 806.2931 must be savedeach year Note: A formula to obtain a present value: Vpresent = Vfuture ( 1 + i)-n    i : anual interest rate n: number of years

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