Question

The cost price of a LCD television is Rs. 24,360. The various schemes for the purchase through installments are given here in the table. Select the best among them.

SI. No.	Schemes	Cost price	Down Payment	Rate of interest	Processing charge	Loan period
01	75% finance	Rs. 24,360	25%	14%	2%	24 month
02	100% finance	Rs. 24,360	Nil %	16%	1%	24 month
03	100% finance	Rs. 24,360	4 EMI	Nil %	2%	24 month

Answer 1

To select the best among the given schemes, we have to calculate EMI and the total amount.
Scheme 01 (75% finance)
Given: Price = Rs. 24,360, down payment = 25%, rate of interest = 14% processing fee = 2%;
Processing charge is 2% of Rs. 24,360
$=\frac{2}{100}\times 24360=487.2\approx Rs.487$.
Down payment is 25% of Rs. 24,360
$=\frac{25}{100}\times 24360=Rs.6,090.$
Hence,
amount P = 24,360 - 6,090 = Rs. 18,270
We can calculate EMI using the formula
$I=\frac{P(2nR+2400)}{n(2400+(n-1\left)R\right)}$.
Therefore
$I=\frac{18270\left[\right(2\times 24\times 14)+2400]}{24[2400+(23\times 14\left)\right]}=\frac{18270\times 3072}{24\times 2722}\approx Rs.859.10$
Total amount to be paid is down payment + processing charge + (EMI $\times$ 24)
$=6090+487+(859.10\times 24)\approx Rs.27195.$
Scheme 02 (100% finance)
Processing fee = 1% of Rs. $24,360=\frac{1}{100}\times 24,360\approx Rs.244$;
down payment = nil; rate of interest = 16%; n = 24.
We calculate EMI using the earlier formula:
$I=\frac{P(2nR+2400)}{n(2400+(n-1\left)R\right)}=\frac{24360\left[\right(2\times 24\times 16)+2400]}{24[2400+(23\times 16\left)\right]}$
We obtain
$I=\frac{24360\times 3168}{24\times 2768}\approx Rs.1,161.70$
Hence the total amount to be paid in this scheme is $244+(1161.70\times 24)\approx Rs.28,125$.
Scheme 03 (100% finance)
Here, there is no interest. Hence EMI amount is given by
$I=\frac{P}{n}=\frac{24360}{24}=Rs.1,015$.
Also the processing fee is 2% of 24,360 which is about Rs. 487. The down payment is
$4I=4\times 1015=Rs.4,060$.
Thus the total amount that would be payable in this scheme is
$4060+487+(24\times 1015)=Rs.28,907$
Compare the amount to be paid under these three schemes. It is the least in scheme 01.
Thus the scheme 01 is more beneficial than the other schemes.