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.
What is the value of the original lease contract?
~~~~~~~~~~~~~~



        In this my post,  I will solve part  (a),  ONLY.



<pre>
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*(r/(1-(1+r)^(-n)))}}},    (1)


where P is the loan amount; r = {{{0.15/12}}} 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 = {{{0.15/12}}}.


Substitute these values into the formula and get this equation

    762.79 = {{{P*(((0.15/12))/(1-(1+0.15/12)^(-72)))}}}.    (2)


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

    {{{((0.15/12))/(1-(1+0.15/12)^(-72))}}} = 0.021145013  (rounded).


Now from equation (2), find the <U>ANSWER</U>

    P = {{{762.79/0.021145013}}} = 36074.23.


<U>ANSWER</U>.  The value of the original lease contract is  $36074.23.
</pre>

Solved.