Question

The overhead costs in a highly automated factory are expected to increase at an annual compound rate of 10 percent for the next 7 years. The overhead cost at the end of the fi rst year is $200,000. What is the annual worth of the overhead costs for the 7-year period? The time value of money rate is 8 percent/year.

Answer 1

Answer:

The annual worth of the overhead costs for 7 year-period is

A = $389743.42.

Then the time value of the annual worth is discounted by 8%

∴  $389743.42 x 0.08 = $31179.47.

Explanation:

Using the formula

A = P(1 + r/n)${nt}$

Where:

A = ?

t = 7

P = $200,000.00

r = 10%

n= 1

TVM =8%

∴ A = $200,000.00(1 + 0.10/1)${1 * 7}$

A = $200,000.00(1.10)${7}$

A = $200,000.00(1.9487171)

A = $389743.42

Then the time value of the annual worth is discounted by 8%

∴  $389743.42 x 0.08 = $31179.47

Answer 2

Answer:

The annual worth of the overhead costs for 7 year-period is given as = $389743.42.

The time value of the annual worth is discounted by 8% is given as $389743.42 x 0.08 = $31179.47.

Explanation:

Let’s recall from the formula,

Given as A = P(1 + r/n)nt

Where A= not known

t = 7, time frame for a 7-year period  

P = $200,000.00

r is the rate = 10%

n= 1

TVM is the time value of money rate =8%

Then  

A = $200,000.00 (1 + 0.10/1) 1x7

A = $200,000.00(1.10) 7

A = $200,000.00(1.9487171)

A = $389743.42

Finding the time value of the annual worth is

389743.42 x 0.08 = $31179.47