A computer is available for Rs 39,000 on cash payment or Rs 19,000 as cash payment followed by five monthly instalments of Rs 4200 each. What is the rate of interest per annum under the instalment plan?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 20%.
SI = PRT/100
Where, SI = Simple interest, P = principal, R = rate and T = time
CP of the computer = Rs 39000
Downpayment = Rs 19000
Remaining balance = 39000 - 19000 = Rs 20000
Amount (for Rs 20000) = 20000 + 20000 × 5/12 × R/100 = 20000 + 250R/3 ---- (1)
⇒ Sum of all the installments for 5 months
⇒ (4200 + SI on 4200 for 4 months) + (4200 + SI on 4200 for 3 months) + (4200 + SI on 4200 for 2 months) + (4200 + SI on 4200 for 1 months) + 4200
⇒ 21000 + (4200 × 10/12 × R/100)
⇒ 21000 + 35R ---- (2)
Now equating equation (1) = equation (2)
⇒ 20000 + 250R/3 = 21000 + 35R
⇒ R = 3000/145 or 20%