Question

The cost of an android mobile phone is Rs. 8,990. Joseph bought it by paying Rs. 500 cash down and the balance he agreed to pay in 10 monthly installments of Rs. 900 each. Nizam bought the same phone by initially paying Rs. 900 and the remaining balance in 8 installments of Rs. 1200 each. Who has paid more rate of interest?

Answer 1

Price of android $=8,990$ Rs.

(i)

Cash down payment by Joseph $=500$ Rs.

Balance $=8990-500=8490$

Number of installments $\left(n\right)=10$

Amount of each installment $\left(I\right)=900$

Amount paid in installments $=10\times 900=9000$

Extra amount paid $\left(E\right)=9000-8490=510$

Rate of interest $=\frac{2400E}{n\left(\right(n+1)I-2E)}$

$=\frac{2400\times 510}{10(11\times 900-2\times 510)}$

$=\frac{2400\times 510}{10\times 880}=13.78$

$\therefore$ Rate of interest $=13.78\%$

(ii)

Cash down payment by Nizam $=900$ Rs.

Balance $=8990-900=8090$

Number of installments $\left(n\right)=8$

Amount of each installment $\left(I\right)=1200$

Amount paid in installments $=8\times 1200=9600$

Extra amount paid $\left(E\right)=9600-8090=1510$

Rate of interest $=\frac{2400E}{n\left(\right(n+1)I-2E)}$

$=\frac{2400\times 1510}{8(9\times 1200-2\times 1510)}$

$=\frac{2400\times 1510}{10800\times 3020}=58.226$

$\therefore$ Rate of interest $=58.22\%$

Hence, Nizam paid more rate of interest.