ation.com Course Materials MHE Reader Orline Chapter 3 Home... For The Cash Flow

Question

ation.com Course Materials MHE Reader Orline Chapter 3 Home... For The Cash Flows Other Math question Civil eng e Online Chapter 3 Homework Saved Help Save & Exit Submit Check my work 2 Problem 03.019 Annual Worth Calculations Find the value of x that makes the equivalent annual worth in years 1 through 10 equal to $700 per year, use an interest rate of 8% per year points The cash flows in year 0 and year 10 has an unknown value x, and 1 through 9 has an annual worth of $700. eBook The value of x is determined to be $6945 Hint Print References 2of 611 Graw Prev Next>

Explanation / Answer

ANSWER:

Equivalent annual worth from year 1 to year 10 = $700

cash flows in year 1 to year 9 = $700

year 0 and year 10 unknown value = x

700 = -year 0 cash flow(a/p,i,n) + cash flow from year 1(a/p,i,n) + cash flow from year 2(a/p,i,n) + cash flow from year 3(a/p,i,n) + cash flow from year 4(a/p,i,n) + cash flow from year 5(a/p,i,n) + cash flow from year 6(a/p,i,n) + cash flow from year 7(a/p,i,n) + cash flow from year 8(a/p,i,n) + cash flow from year 9(a/p,i,n) + year 10 cash flow(f/a,i,n)(a/f,i,n)

i = 8% and n =10 years

700 = -x(a/p,8%,10) + 700(a/f,8%,1) + 700(a/f,8%,2) + 700(a/f,8%,3) + 700(a/f,8%,4) + 700(a/f,8%,5) + 700(a/f,8%,6) + 700(a/f,8%,7) + 700(a/f,8%,8) + 700(a/f,8%,9) + x(a/f,8%,10)

700 = -x * 0.149 + 700 * 1 + 700 * 0.4808 + 700 * .308 + 700 * 0.2219 + 700 * 0.1705 + 700 * 0.1363 + 700 * 0.1121 + 700 * 0.094 + 700 * 0.0801 + x * 0.069

700 = -0.149x + 700 + 336.54 + 215.62 + 155.34 + 119.32 + 95.42 + 78.45 + 65.81 + 56.06 + 0.069x

700 = -0.1641x + 1822.56

0.1641x = 1822.56 - 700

0.1641x = 1122.56

x = 1122.56 / 0.1641

x = $6,841.98 or $6842 approx.

so the value of x is $6842.

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