| Course | MT217 Finance |
|---|---|
| Unit | Unit 5 |
| Paper type | Annuity calculations |
| Length | About 860 words, 6 pages double-spaced |
| Format | APA 7 student paper |
| School | Purdue University Global |
| Program | BS in Business Administration |
| Updated | October 2026 |
Free sample paper for MT217 Unit 5
What One Extra Percentage Point Costs: A Unit 5 Annuity Calculation Set for an HVAC Contractor
[Student Name]
Purdue University Global
MT217: Finance
Unit 5 Annuity Calculations
[Instructor Name]
[Date]
Brightwater Heating and Air, its loans, lease and every figure are composite and illustrative; the sources cited are real.
The Contractor
Brightwater Heating and Air is a composite residential and light commercial HVAC contractor in Knoxville, Tennessee, with nine technicians. This year it needs two new service vans with shelving and a refrigerant recovery setup, at [$96,000] together, and it is weighing a lease on diagnostic equipment and a savings plan for a rooftop unit compressor it will need to replace in four years. All rates are annual and compounded monthly.
Problem 1: The Van Loan at Two Rates
A loan of [$96,000] over 60 months at 7.5 percent has a monthly rate of 0.625 percent. Plugging 96,000, a 0.00625 monthly rate and 60 months into the standard level-payment loan formula, Brightwater's monthly payment comes to [$1,923.64]. Over sixty months the contractor pays [$115,418.58], of which [$19,418.58] is interest.
A second lender quotes 8.5 percent. The payment rises to [$1,969.59], only [$45.94] more each month. Over the loan, that adds about [$2,756.64] in interest.
What it means: a one-point difference looks small per month and costs about the price of a set of recovery tanks and a vacuum pump over five years. The contractor should push for the lower rate or ask the dealer to match it.
Problem 2: Stretching the Term
At 7.5 percent, the same loan stretched to 72 months lowers the payment to [$1,659.85], about [$264] a month less. Total interest rises to [$23,509.26], about [$4,091] more than the 60-month loan.
What it means: the longer term eases monthly cash flow in a slow winter but costs about two months of payments in extra interest. The vans may need replacing around year seven, so a six-year loan would leave the contractor paying for vans that are nearly worn out.
Problem 3: A Lease Paid in Advance
A diagnostic equipment supplier offers a 36-month lease at [$1,450] a month, paid at the start of each month. Payments at the beginning of each period form an annuity due, whose present value is the ordinary annuity value multiplied by one plus the monthly rate. At 7.5 percent, the ordinary annuity value is [$46,614.47]; multiplied by 1.00625, the lease is worth [$46,905.81] today.
What it means: paying in advance makes the lease about [$291] more expensive in present value than the identical 36 payments made in arrears. If a supplier will sell the same equipment outright for under about [$46,900], buying wins at Brightwater's 7.5 percent borrowing rate, before considering maintenance terms in the lease.
Problem 4: Saving for the Compressor
The contractor wants [$30,000] in four years to replace a large rooftop compressor it services under a maintenance agreement, and its savings account pays 4.2 percent. A sinking fund calculation, the future value annuity solved for the payment, sets the deposit. With a monthly rate of 0.35 percent over 48 months, the deposit is [$575.06] a month.
What it means: about [$575] a month, roughly a third of one van payment, builds the full amount. Starting a year later would push the deposit above [$780] a month to reach the same target in three years. The account's 4.2 percent rate also matters: at 2 percent, the four-year deposit would be about [$600] a month, so shopping for a better savings rate is worth an afternoon.
How the First Payment Splits
In month one of the 60-month van loan, [$600.00] of the [$1,923.64] payment is interest on the full [$96,000], and [$1,323.64] goes to principal. As the balance shrinks, so does the interest portion of every later payment, and by month sixty almost the whole payment is principal. That is why an extra payment early in the loan saves far more interest than the same extra payment in year five.
The pattern also matters for Brightwater's tax records. Only the interest part of each payment is a deductible expense, so the deduction is largest in the first year and smaller each year after, while depreciation on the vans follows its own schedule.
Forty-six dollars a month sounds like nothing; over five years it is twenty-seven hundred.
Summary
Brigham and Houston (2019) present annuities as the tool for comparing streams of level payments, and Ross et al. (2022) stress that the total cost of borrowing depends as much on the term as on the rate. Brightwater's choices show both. The one-point rate difference costs about [$2,757], the extra year costs about [$4,091], and the timing of lease payments changes the cost by a few hundred dollars. The best combination is the 60-month loan at the lower rate, buying the diagnostic equipment if a price below its lease value can be found, and starting the compressor deposits this month. Graham and Harvey (2001) found that many firms rely on simple rules of thumb for such choices, which is why setting out the full cost of each option is useful even for a small contractor.
References
Brigham, E. F., & Houston, J. F. (2019). Fundamentals of financial management (15th ed.). Cengage.
Graham, J. R., & Harvey, C. R. (2001). The theory and practice of corporate finance: Evidence from the field. Journal of Financial Economics, 60(2-3), 187-243. https://doi.org/10.1016/S0304-405X(01)00044-7
Ross, S. A., Westerfield, R. W., & Jordan, B. D. (2022). Fundamentals of corporate finance (13th ed.). McGraw-Hill.
What the MT217 Unit 5 assignment asks for
The fifth unit usually asks for annuity problems: loan payments, total interest, present values of payment streams, annuities due and savings plans. Most prompts want each problem set out with the known values, the formula or calculator inputs and the answer. Watch the timing of payments, since a lease or rent paid at the start of each period is an annuity due and must be valued differently from a loan paid at the end. Keep rates and periods in the same unit, usually months for loans and leases. Many sections reward comparing options, such as two rates or two terms, and stating which is better and why. A short amortization example, showing how one payment splits between interest and principal, is common. Four pages is typical, with every numbered problem closing on what its answer changes for the business.
Inside the MT217 Unit 5 example
The set introduces the contractor and its four decisions, then states that all rates are compounded monthly. Problem 1 computes the van payment at 7.5 percent, totals the interest and reprices the loan at 8.5 percent, translating the difference into equipment the contractor could buy. Problem 2 stretches the term to 72 months and weighs the lower payment against the higher interest and the vans' useful life, which a margin note highlights. Problem 3 values a 36-month lease paid in advance as an annuity due and compares it with paying in arrears and with buying outright. Problem 4 sets the monthly deposit for a compressor fund and shows the cost of waiting a year or accepting a lower savings rate. A section on the first payment shows the interest and principal split and the tax effect. The highlighted line puts $46 a month against $2,700, and the summary ranks the options.
MT217 Unit 5 rubric: what earns full points
Annuity sets are generally graded on correct setup, especially the timing of payments, and on clear interpretation. Matching the rate and the number of periods to the payment frequency earns method credit, and mixing monthly payments with annual rates is the most common error graders look for. Annuities due must be identified and valued correctly. Comparing options with total cost, not only monthly payment, shows understanding of what borrowing really costs. An amortization example demonstrates how interest and principal change over a loan's life. Each answer should be followed by a sentence explaining what it means for the business. A summary that ranks options and recommends one adds analytical value beyond the arithmetic. Calculator or spreadsheet inputs should be visible, and the textbook and the Graham and Harvey survey belong in the reference list.
Common MT217 Unit 5 mistakes, and how to avoid them
Annuity problem sets most often lose points by valuing payments made at the start of each month as if they came at the end, which understates the value of payments made in advance. Another frequent mistake is using an annual rate with monthly periods. Some students compare loans by monthly payment alone and miss the total interest. Others compute a payment correctly but never say which option is better. Amortization is sometimes shown without explaining why the interest share falls. Watch rounding, which can shift a sixty-month total by several dollars. If you use Excel's PMT or PV functions, list the arguments so a grader can follow them. If your section gives problems without a business context, adding one sentence of meaning after each answer still helps. If you paste the van, lease or savings questions from your own prompt, a writer can set each one up with its timing marked.
Get an MT217 Unit 5 example written to your instructions
Paste in the Unit 5 problems as assigned and the rubric, noting whether your section expects formulas, calculator entries or spreadsheet functions. Solutions name each annuity type, state the monthly rate and period count, and compare results wherever the prompt allows. That opening sample is on the house, usually within 24-48h. The paper above is an original model document written by our desk, not a submitted student paper and not an official Purdue University Global document.
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MT217 Unit 5 questions, answered
How do I know whether a problem is an annuity due?
Look at when the first payment happens. If it falls today, at the start of the first period, as rent and most leases do, it is an annuity due. If it falls at the end of the first period, as loan payments usually do, it is ordinary. The sample names the type in the first line of every problem so the choice is visible.
Why does a longer loan cost more if the payment is lower?
Because the balance stays outstanding longer and accrues interest for more months. In the sample, 72 payments of 1,659.85 total 119,509.26 against 115,418.58 for 60 payments, even at the same rate. A lower payment helps monthly cash flow, and the paper notes that benefit, but the total cost rises by more than a full point of interest would add.
Can I use the PMT function in Excel?
Usually, and many sections encourage it. Keep the rate and the number of periods monthly inside the function, and show the arguments rather than only the result. The sample writes out the formula for each problem and would note the equivalent function as a check. If your instructor wants the work by hand, the custom version shows every step.
Where can I find a free MT217 Unit 5 sample paper?
A complete MT217 Unit 5 annuity calculation set appears on this page. It prices a van loan at two rates and two terms, values a lease paid in advance, plans a savings fund and shows an amortization split, with margin notes.
How much does one percentage point cost on the van loan?
At 8.5 percent instead of 7.5, the payment rises about $45.94 a month. Over sixty months that adds about $2,757 in interest, roughly the cost of a recovery tank and vacuum pump set.