A computer is available for Rs. 39,000 on cash payment or Rs. 19,000 as cash payment followed by five monthly installments of Rs. 4,200 each. What is the rate of interest per annum under the instalment plan?

Calculation:

Total cost of the computer = Rs. 39000

Down payment = Rs. 19000

Balance = Rs. (39000 - 19000) = Rs. 20000.

Let the rate of interest be R% p.a.

Amount of Rs. 20000 for 5 months

=Rs.( 20000 + 20000 × 5/12 × R/100)=Rs.(20000+250R/3)

The customer pays the shopkeeper Rs. 4200 after 1 month,

Rs. 4200 after 2 months, ...... and Rs. 4200 after 5 months.

Thus, the shopkeeper keeps Rs. 4200 for 4 months, Rs. 4200 for 3 months, Rs. 4200 for 2 months, Rs. 4200 for 1 months and Rs. 4200 at the end.

∴ sum of the amounts of these installments

⇒  (Rs. 4200 + S.I. on Rs 4200 for 4 months) + (Rs. 4200 + S.I. on Rs. 4200 for 3 months) + ...... + (Rs. 4200 + S.I. on Rs. 4200 for 1 month) + Rs. 4200

⇒ Rs. (4200 × 5) + S.I. on Rs. 4200 for (4 + 3 + 2 + 1) months

⇒ Rs. 21000 + S.I. on Rs. 4200 for 10 months

⇒ Rs.(21000 + 4200 × R × 10/12×1/ 100)

⇒ (21000 + 35R)

(20000+250R/3) =  (21000 + 35R)

R = \(20\frac{20}{29}\)%
Alternate Method Total amount = 39000

Down payment = 19000

Remaining amount = 20000

Installment = 4200

So,

Principal 

At Starting         =   20000

after 1 month →  20000 - 4200 = 15800

After 2 months → 15800 - 4200 = 11600

After 3 months →  11600 - 4200 = 7400

After 4 months →  7400 - 4200 = 3200

So, 

total principal = 20000 + 15800 + 11600 + 7400 + 3200 = 58000

and

Interest = 4200 × 5 - 20000 = 1000

So,

rate of interest for 1 month = (1000/58000) × 100 = 100/58 = (50/29)%

rate of interest for 12 months or annual rate of interest = 12 ×  (50/29)% = (600/29)%