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27) Cooley Landscaping Company needs to borrow $30,000 for a new front-end dirt loader. The bank is willing to loan the funds at 8.5% interest with annual payments at the end of the year for the next ten years. The loan is fully amortized, i.e., the loan will be fully paid off at the end of year ten. What is the annual payment on this loan for Cooley Landscaping?

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Answer:

The annual payment at the end of each year: $4,572.23

Explanation:

The formular for calculating Present value of Annuity is applied in this case to help us find the equal annual payment.

Applying information in the question, we have the annuity that have:

n= 10 as there are 10 equal annual payments paid at the end of each year during 10 years;

i = 8.5% per annum compounded annually, as stated in the question;

PV = Borrowed amount = $30,000;

C = the equal annual payment.

The formular for PV of Annuity: PV = (C/i) x [ 1- (1+i)^(-n)] <=> C = (PV x i) / [ 1- (1+i)^(-n)]

Thus, C = (30,000 x 8.5%) / [ 1- 1.085^(-10) ] = $4,572.23

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