This is an extra credit question Completing this question is

This is an extra credit question. Completing this question is optional. Please note the wording on this problem is a little unclear. Dr. Shelf will pay maintenance for a total of 5 years (so the end of years 5. 6. 7. 8.9). Professor Shelley is creating a budget for her recently awarded research grant. Her research requires a heavy-duty generator that has an initial cost of $39135. She estimates she will need to pay for maintenance on the generator beginning at the end of year 5. She will pay maintenance costs each year for the next 5 years. At that point, she will either scrap her research or submit a new research proposal. She estimates the first year of maintenance will cost $497. with the maintenance costs increasing by $77 per year for each year after that. How much should she put in her budget for maintenance costs? She is using a 5% interest rate. Enter your answer as follows: 1234 Round your answer. Do not use a dollar sign (\"$\"), any commas (\", \"). or a decimal point (\".\").

Solution

Answer:

Professor Shelley needs to pay for maintenance only at the end of year 5 for the next 5 years. (i.e. 6th, 7th, 8th, 9th and 10th years).

The maintenance cost for the 6th year is $497 and it increased by $77 per year (are as follows).

Therefore,
6th year : $497
7th year : $497 + $77 = $574
8th year : $574 + $77 = $651
9th year : $651 + $77 = $728
10th year : $728 + $77 = $805

Thus, the total cost of maintenance = $497 + $574 + $651 + $728 + $805 = $3255 (in dollars)

Since the interest can be calculated as
$3255 x 0.05 = $162.75 (in dollars)

Therefore, she should put in her budget for maintenance = $3255 + $162.75 = $3417.75

The number 3417.75 is rounded to the nearest integer is 3418. So the answer to entered is 3418.