A mobile phone is available for ₹79,860 by cash payment or by paying cash of ₹60,000 as down payment and the remaining amount in three equal annual instalments. If the shopkeeper charges interest at the rate of 10% per annum compounded annually, then the amount of each instalment (in ₹) will be:
Answer & explanation
Correct answer: option 1
Remaining amount to be paid in installments = 79860 - 60000 = 19860
Let us assume that amount of each installment = Rs. X
ATQ,
19860 = \(\frac{X}{1+10/100}\) +\(\frac{X}{(1+10/100)²}\) + \(\frac{X}{(1+10/100)³}\)
19860 = \(\frac{X}{11/10}\) +\(\frac{X}{(11/10)²}\) + \(\frac{X}{(11/10)³}\)
19860 = \(\frac{X}{11/10}\) +\(\frac{X}{121/100}\) + \(\frac{X}{1331/1000}\)
X = 19860 × \(\frac{1331}{3310}\)
X = 7986
So, Each installment to be paid = Rs. 7986