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sergij07 [2.7K]
3 years ago
12

On January 1, 1997, an investment account is worth 100,000. On April 1, 1997, the value has increased to 103,000 and 8,000 is wi

thdrawn. On January 1, 1999, the account is worth 103,992. Assuming a dollar weighted method for 1997 and a time weighted method for 1998, the annual effective interest rate was equal to x for both 1997 and 1998.Calculate x.(A) 6.0% (B) 6.25% (C) 6.50% (D) 6.75% (E) 7.0%
Business
1 answer:
loris [4]3 years ago
4 0

Answer:

(B) 6.25%

Explanation:

January 1, 1997 = $100,000

April 1. 1997 = $103,000 - $8,000 = $95,000

January 1, 1999 = $103,992

annual interest rate for 1997 = i = (x - 100,000 + 8,000) / [100,000 - 8,000(1 - ³/₁₂) = (x - 100,000 + 8,000) / [100,000 - 8,000(1 - 0.25) = (x - 92,000) / 94,000

x = 92,000 + 94,000i

annual interest rate for 1998 = 1 + i = 103,992/x

x = 103,992/(1 + i)

0 = x(1 + i) - 103,992

now we replace x by 92,000 + 94,000i

0 = (92,000 + 94,000i)(1 + i) - 103,992

0 = (94,000 (1 + i) - 2,000)(1 + i) - 103,992

we now replace 1 + i by Y

0 = (94,000Y - 2,000)Y - 103,992

0 = 94,000Y² - 2,000Y - 103,992

using a calculator, Y = 6.25%

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The missing part of the question is found below:

Boots Plus has two product lines: Hiking boots and Fashion boots. Income statement data for the most recent year follow:

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Sales revenue       $480,000 $340,000 $140,000

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Answer

By discontinuing fashion line of business operating income would increase by $5,000

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The impact of eliminating Fashion line is evident in the revised Income statement below:

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Sales revenue                                         $340,000

Variable expenses                                  ($235,000)

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Fixed expenses($76,000-$25,000)     ($51,000)

Operating income                                    $54,000

By discontinuing the fashion line of business,the operating income would increase by $5,000 ($54,000-$49,000) from $49,000 when operating the two lines of business to $54,000 when fashion is closed up.

The most appropriate action is to concentrate on the hiking line which might mean that Boots plus has a competitive edge in the Hiking business sector.

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top-of-mind awareness

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