Professor Shelley is creating a budget for her recently awarded research grant.

Question

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 $39180. 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 $453, with the maintenance costs increasing by $74 per year for each year after that. How much should she put in her budget for maintenance costs? She is using a 5% interest rate. Enter your answer as follows: 1234 Round your answer. Do not use a dollar sign ("$"), any commas (", "), or a decimal point (".").

Explanation / Answer

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

The maintenance cost for the 6th year is $453 and it increases by $74 each year after that. Therefore, the maintenace cost for each of these years are as follows:

6th year: $453
7th year: $453 + $74 = $527
8th year: $527 + $74 = $601
9th year: $601 + $74 = $675
10th year: $675 + $74 = $749

Thus, the total maintenance cost, in dollars = 453 + 527 + 601 + 675 + 749
= 3,005

Since she is using a 5% interest rate, the interest amount can be calculated as:

3005 x 0.05
= 150.25

Therefore, the amount, in dollars, she should put in her budget for maintenance
= 3,005 + 150.25
= 3,155.25
The number 3,155.25 rounded to the nearest integer is 3,155. So the answer to be entered is 3155.

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