Question 1193609
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A second-hand car was bought for ₱100,000 downpayment and 
monthly installments of ₱10,000 to be paid for 4 years. What is the 
cash price of the car if money is worth 12% compounded monthly?
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        Calculations in the post by @yurtman are incorrect.

        I came to provide correct calculations.



<pre>
To calculate the cash price of the car, we need to find the present value of the monthly installment 
payments and add the downpayment.


        Step 1: Formula for Present Value of an Annuity


The formula for the present value of an annuity is:


    PV = {{{M*((1 - (1 + r)^(-n))/r))}}}


Where:  
    PV  = present value of the monthly installments (the amount equivalent to these payments today)  
    M   = monthly payment (10,000)
    r   = monthly interest rate (0.12/12} = 0.01)  
    n   = total number of payments (48 = 4*12)  

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        Step 2: Calculate the Present Value of Installments


Substitute the known values:

    PV = {{{10000*((1 - (1 + 0.01)^(-48))/0.01)}}} = 379739.60   <<<---===  about one order more than in the post by @yurtman 
                                                                 I performed this calculation using my Excel spreadsheet


So:

   PV = 379739.60

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        Step 3: Add the Downpayment


The total cash price of the car is:

    Cash Price = Downpayment + PV = 100,000 + 379739.60 = 479739.60


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        Final Answer:


The cash price of the car is approximately 479739.60.
</pre>

Solved correctly.