Question
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Present value with periodic rates. Cooley Landscaping needs to borrow for a new front-end
dirt loader. The bank is willing to loan the money at interest for the next 7 years with annual,
semiannual, quarterly, or monthly payments. What are the different payments that Cooley Landscaping
could choose for these different payment plans?
What is Cooley’s payment for the loan at interest for the next 7 years with annual payments?
(Round to the nearest cent.)

Ask by Dawson Mccoy. in the United States
Jan 24,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

Cooley Landscaping’s annual payment for a $26,000 loan at 7% interest over 7 years is $140,121.52.

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Bonus Knowledge

To find Cooley Landscaping’s payment for the loan with annual payments, we can use the formula for the present value of an annuity:
where:
  • is the present value ($26,000),
  • is the payment,
  • is the interest rate per period (0.07 for annual payments),
  • is the total number of payments (7 years).
Rearranging the formula to solve for :
Substituting in the values:
Calculating the denominator:
Now calculating the payment:
Therefore, Cooley Landscaping’s annual payment at interest for the next 7 years is approximately .
For semiannual, quarterly, and monthly payments, the value of would change accordingly (dividing the annual interest by the number of periods per year), and would also increase (multiplying years by the number of periods per year). Each payment plan can be calculated similarly using the present value annuity formula.

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