SOLUTION: Yankee Construction agreed to lease payments of $762.79 on construction equipment to be made at the end of each month for six years. Financing is at 15% compounded monthly. a) W

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Question 1207542: Yankee Construction agreed to lease payments of $762.79 on construction equipment to be made at the end of each month for six years. Financing is at 15% compounded monthly.
a) What is the value of the original lease contract?
b) If, due to delays, the first eight payments were deferred, how much money would be needed after nine months to bring the lease payments up to date?
c) How much money would be required to pay off the lease after nine months?
d) If the lease were paid off after nine months, what would the total interest be?
e) How much of the total interest would be due to deferring the first eight payments?
Answer by ikleyn(52915) About Me  (Show Source):
You can put this solution on YOUR website!
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Yankee Construction agreed to lease payments of $762.79 on construction equipment to be made
at the end of each month for six years. Financing is at 15% compounded monthly.
What is the value of the original lease contract?
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        In this my post,  I will solve part  (a),  ONLY. 


In this problem, the value of the original lease contract is the amount of a loan, which requires 
monthly payments of $762.79 at the end of each month for six years at 15% compounded monthly.


Use the standard formula for monthly payments of a loan

    M = P%2A%28r%2F%281-%281%2Br%29%5E%28-n%29%29%29,    (1)


where P is the loan amount; r = 0.15%2F12 is the effective interest rate per month;
n is the number of payments (same as the number of months, n = 6*12 = 72);
M is the monthly payment.


In this problem  M = $762.79;  r = 0.15%2F12.


Substitute these values into the formula and get this equation

    762.79 = P%2A%28%28%280.15%2F12%29%29%2F%281-%281%2B0.15%2F12%29%5E%28-72%29%29%29.    (2)


In equation (2), calculate separately the coefficient (the multiplier, or the factor)

    %28%280.15%2F12%29%29%2F%281-%281%2B0.15%2F12%29%5E%28-72%29%29 = 0.021145013  (rounded).


Now from equation (2), find the ANSWER

    P = 762.79%2F0.021145013 = 36074.23.


ANSWER.  The value of the original lease contract is  $36074.23.

Solved.