Question

A builder plans to sale of flats each for cash Rs 30,00,000 or Rs 10,31,600 cash down payment and three equal quarterly installment.If the rate of the interest is 10% per annum compounded quarterly,compute the value of each installment under the installment scheme.Also find the total interest.

Answer 1

Solution :-

Given-
 Flat cost cash price = Rs 30,00,000

 Cash down payment = Rs 10,31,600

So, The remaining amount to be paid in installment
  
= Rs 30,00,000 - Rs 10,31,600

= Rs 1968400
 
Let installment in each quarter be x
then
 A= P(1+r/100)∧n

As the quarterly installment will be same and it includes principal and interest.Hence the value of principal must be different.

Let the three quarterly amount principals are  P1,P2 and P3 such that-
   
  P1+P2+P3 = 1968400

since rate is 10% per annum, So per quarter it is 10/4 = 2.5%

Let x = the amount to be paid per quarter means installment.

so,
         x = P1 (1+2.5/100)∧1

 so, P1 = x * 0.9756

similarly,  

       P2= x * 0.9756^2
       P3= x * 0.9756^3
Now,
since  
         P1+P2+P3 = 1968400

so,
   x*(0.9756)  +  x*(0.9756)^2 +  x*(0.9756)^3 = 1968400

x [ 0.9756+ 0.9518 + 0.9286] = 1968400

so, x=  1968400 /2.856  = 689215.686
 
hence  the value of each installment is Rs 689215.686


and the total interest is [ 689215.686*3 - 1968400 ]
 
i.e The total interest = Rs 99247.06

Answer 2

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