Question

Average accumulated expenditures for year five on a construction project amounted to $70,000. The total cash invested in the project by the end of year five, was $160,000. During year six, the firm spent another $240,000 (total) on the project, uniformly throughout the year. Compute average accumulated expenditures for year six.

Answer 1

Answer:

120,000

Explanation:

As the expenditures occur uniformly throughout the period then, the weighted average expenditures will be equal to half the expenditures as the weights could be arrange to demostrate:

being a the amount spend per  time diffrencial (n) 240,000/n

we have the formula of n terms:

$a(x/n) + a(x-1))/n + a(x-2/n) + ... + a(3/n) + a(2))/n + a(1/n) +a (0/n)\\ We arrengle as follows:\\a(x/n) +a (0/n) + a(x-1))/n + a(1/n) + a(x-2/n) + a(2))/n\\each pair of term adds to:\\a(x/n)\\which is the simple average$

As we have half the terms then this is multiply by n/2

$a(x/n) \times n/2 = a(x/2)$