A Bluetooth speaker is sold for ₹3,500 cash, or ₹1,000 cash down payment and the balance in 3 equal annual instalments. If rate of interest is 12.5% per annum and interest is compounding annually, then find the amount of instalment. (correct to 2 decimal places)
Show answer & explanation
Correct answer: C
Explanation
The Correct answer is Option 3 i.e. ₹1,049.83.
C.I. = P(1 + R/100)T - P
And,
Total amount = E/(1 + 12.5/100) + E/(1 + 12.5/100)2 + E/(1 + 12.5/100)3 + ......+ E/(1 + 12.5/100)n
where, P = Principal, R = Rate, T = Time and, E = Each Installment
Amount to be paid in installments = 3500 - 1000 = Rs.2500
⇒ 2500 = E/(1 + 12.5/100) + E/(1 + 12.5/100)2 + E/(1 + 12.5/100)3
⇒ 2500 = E/(1 + 1/8) + E/(1 + 1/8)2 + E/(1 + 1/8)3
⇒ 2500 = E/(9/8) + E/(9/8)2 + E/(9/8)3
⇒ 2500 = 8E/9 + 64E/81 + 512E/729
⇒ 2500 = 648E/729 + 576E/729 + 512E/729
⇒ 2500 = (648E + 576E + 512E)/729
⇒ 2500 = 1736E/729
⇒ E = Rs.1049.83