Question

The operating and maintenance expenses for a mining machine are expected to be $11,880 in the first year and increase by $864 per year during the 15-year life of the machine. What uniform series of payments would cover these expenses over the life of the machine

Answer 1

To cover the operating and maintenance expenses for the mining machine over its 15-year life, a uniform series of payments can be calculated using the concept of uniform series Present Worth.

Step-by-step explanation:

To find the uniform series of payments that would cover the operating and maintenance expenses for the mining machine over its 15-year life, we can use the concept of uniform series Present Worth. The initial expense of $11,880 can be considered as the present worth of the uniform series. The annual increase of $864 can be considered as an additional uniform series with a growth perpetuity formula. Using these values, we can calculate the uniform series of payments that would cover the expenses over the life of the machine.

Answer 2

The answer is "
`\$16,441`".

Step-by-step explanation:

First-year operational and maintenance costs
`= \$11,880`.

Operating and repair costs increase inwards
`=\$864` for the first year

N =15 years machine life

Interest
`I = 10\%`annually combined

Please find the image file.

Its single payment sequence is now provided by:

`Amount=(\text{15-year system quantity})* (\frac{\text{Rate of interest}}{(1-(1+ \text{Rate of interest})- n))}`

`= \$522,371.3236 * ((0.1)/((1-(1+0.1)-15)))\\\\`

Uniform payment sequence
`=\$16441.2477 \approx\$16,441`