A TV set is available for ₹19,650 in cash or for ₹3,100 as a cash down payment and three equal annual instalments. If the shopkeeper charges interest at the rate of 10% per annum compounded annually, calculate the amount of each instalment.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. ₹6,655.
Present value of instalment = a/(1 + R/100)n
Amount to be paid in installments = 19650 – 3100 = 16550
Let each installment = a
16550 = a/(1 + 10/100) + a/(1 + 10/100)2 + a/(1 + 10/100)3
⇒ 16550 = a/(11/10) + a/(121/100) + a/(1331/1000)
⇒ 16550 = a × 10/11 + a × 100/121 + a × 1000/1331
⇒ 16550 = a(10/11 + 100/121 + 1000/1331)
⇒ 16550 = a(310/1331)
⇒ a = 16550 × 1331/3310 = 6655