A bike is sold by an automobile agency for rupess $19200$ cash or for $ 4800$ cash downpayment

Question

Problem : A bike is sold by an automobile agency for rupess $19200$ cash or for $ 4800$ cash downpayment together with $5$ equal monthly installment if rate of interest charged by the company is $12%$ per annum .find the amount of the installment

solution: amount after downpayment $= 14400$

simple interest= $720$

Amount $= 14400+720$

= $15120$

installment =$3024$

Am I right ??

Answer 1

Some hints:

• The monthly interest rate is $i_m=\frac{i}{12}=0.01$

• The future value of the five installments is

  $$\sum_{k=0}^4 x\cdot (1+i\cdot k) =(5+10\cdot i)\cdot x=5.1x$$

• The future value of $19,200$ cash and $4,800$ cash are $ 19,200\cdot (1+0.01\cdot 5)$ and $4,800\cdot (1+0.01\cdot 5)$ respectively.

• The future value of the five installments and $4,800$ has to be equal to the future value of $19,200$.