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 instalments.If the rate of the interest is 10% per annum compounded quarterly,compute the value of each instalment under the instalment scheme. Also find the total interest.

Answer 1

given things r as follows :-
 Flat cost cash price = Rs 30,00,000
Cash down payment = Rs 10,31,600
⇒ 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
now,
 A= P(1+r/100)∧n
the quarterly installment will be same and it includes principal and interest.∴the value of principal must be different.
let the three quarterly amount principals are  P₁,P₂ and P₃ such that-
    P₁+P₂+P₃ = 1968400
as we know da 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.
therefore
         x = P₁ (1+2.5/100)∧1 
∴ P₁ = x * 0.9756

again, 
P₂= x * 0.9756²
       P₃= x * 0.9756³
 as we know, P₁+P₂+P₃ = 1968400
again,
   x*(0.9756)  +  x*(0.9756)^2 +  x*(0.9756)^3 = 1968400 
x [ 0.9756+ 0.9518 + 0.9286] = 1968400
 x=  1968400 /2.856  = 689215.686
 ⇒ the value of each installment is Rs 689215.686
and the total interest is [ 689215.686*3 - 1968400 ]
 ∴ the total interest = Rs 99247.06