Question

The cost price of an LCD television is Rs. 24,360. The various schemes for the purchase through instalments 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 months
02	100% finance	Rs. 24,360	Nil%	16%	1%	24 months
03	100% finance	Rs. 24,360	4 EMI	Nil%	2%	24 months

Answer 1

Hint: We will find the total amount paid in each scheme. For each scheme, first of all, we will calculate the processing charge followed by down payment that will be paid during the purchase of T.V. Then we need to calculate the EMI paid each month on the amount left using the formula $I = \dfrac{{P\left( {2nR + 2400} \right)}}{{n\left( {2400 + \left( {n - 1} \right)R} \right)}}$. Finally, we will calculate the total amount paid by adding down payment, processing charge and amount paid as EMI in 24 months. The scheme in which the total amount paid will be minimum is considered as the best scheme among others.

Complete step by step answer:

We will calculate the total amount that a person needs to pay in each scheme.
For the first scheme when T.V. is 75% finance, we are given that, the cost price is Rs 24,360, down payment is 25%, rate of interest is 14% and processing fee is 12%.
First we calculate the processing charge as,
2% of 24,360
$\dfrac{2}{{100}} \times 24360 = 487.2$, approximately equals to Rs 487.
Now, we shall calculate the amount of money paid during the purchase, that is down payment for the given scheme, which is 25% of Rs 24,360
$\dfrac{{25}}{{100}} \times 24360 = 6,090$
If the customer has already paid Rs 6,090 from the total price of the T.V., then find the amount left on which the customer would pay rent.
Amount left=Rs 24,360-Rs 6,090=Rs 18,270
Now, we will calculate EMI from the given formula, $I = \dfrac{{P\left( {2nR + 2400} \right)}}{{n\left( {2400 + \left( {n - 1} \right)R} \right)}}$, $P$ is the amount on which the EMI is paid, $n$ is the number of months and $R$ is the rate of interest.
$I = \dfrac{{18270\left( {2\left( {24} \right)\left( {14} \right) + 2400} \right)}}{{\left( {24} \right)\left( {2400 + \left( {24 - 1} \right)\left( {14} \right)} \right)}}$
Solve the expression as, $I = \dfrac{{18270 \times 3072}}{{24 \times 2722}} \approx {\text{Rs }}859.10$
Now calculate the total amount paid inn 24 months is ${\text{Rs }}859.10 \times 24 \approx {\text{Rs }}20,618$
We have to calculate the total amount paid including down payment, processing charge and amount paid as EMI in 24 months.
6090 +487+20,618=Rs 27,195
For the first scheme when T.V. is 75% finance, we are given that, the cost price is Rs 24,360, down payment is 25%, rate of interest is 14% and processing fee is 12%.
First we calculate the processing charge as,
2% of 24,360
$\dfrac{2}{{100}} \times 24360 = 487.2$, approximately equals to Rs 487.
Now, we shall calculate the amount of money paid during the purchase, that is down payment for the given scheme, which is,
25% of Rs 24,360
$\dfrac{{25}}{{100}} \times 24360 = 6,090$
If the customer has already paid Rs 6,090 from the total price of the T.V., then find the amount left on which the customer would pay rent.
Amount left=Rs 24,360-Rs 6,090=Rs 18,270
Now, we will calculate EMI from the given formula, $I = \dfrac{{P\left( {2nR + 2400} \right)}}{{n\left( {2400 + \left( {n - 1} \right)R} \right)}}$, $P$ is the amount on which the EMI is paid, $n$ is the number of months and $R$ is the rate of interest.
$I = \dfrac{{18270\left( {2\left( {24} \right)\left( {14} \right) + 2400} \right)}}{{\left( {24} \right)\left( {2400 + \left( {24 - 1} \right)\left( {14} \right)} \right)}}$
Solve the expression as, $I = \dfrac{{18270 \times 3072}}{{24 \times 2722}} \approx {\text{Rs }}859.10$
Now calculate the total amount paid inn 24 months is ${\text{Rs }}859.10 \times 24 \approx {\text{Rs }}20,618$
We have to calculate the total amount paid including down payment, processing charge and amount paid as EMI in 24 months.
6090 +487+20,618=Rs 27,195
For the second scheme when T.V. is 100% finance, we are given that, the cost price is Rs 24,360, down payment is Nil, rate of interest is 16% and processing fee is 1%.
First we calculate the processing charge as,
1% of 24,360
$\dfrac{1}{{100}} \times 24360 = 243.60$, approximately equals to Rs 244.
Since the down payment is Nil, the customer will pay EMI on Rs 24,360
Now, we will calculate EMI from the given formula, $I = \dfrac{{P\left( {2nR + 2400} \right)}}{{n\left( {2400 + \left( {n - 1} \right)R} \right)}}$, $P$ is the amount on which the EMI is paid, $n$ is the number of months and $R$ is the rate of interest.
$I = \dfrac{{24360\left( {2\left( {24} \right)\left( {16} \right) + 2400} \right)}}{{\left( {24} \right)\left( {2400 + \left( {24 - 1} \right)\left( {16} \right)} \right)}}$
Solve the expression as, $I = \dfrac{{24360 \times 3168}}{{24 \times 2768}} \approx {\text{Rs 1,161}}.70$
Now calculate the total amount paid inn 24 months is ${\text{Rs 1161}}.70 \times 24 \approx {\text{Rs }}27,881$
We have to calculate the total amount paid including down payment, processing charge and amount paid as EMI in 24 months.
0 +244+27,881=Rs 28,125

For the third scheme when T.V. is 100% finance, we are given that, the cost price is Rs 24,360, down payment is Nil, rate of interest is also Nil and processing fee is 2%.
First we calculate the processing charge as,
2% of 24,360
$\dfrac{2}{{100}} \times 24360 = 487.2$, approximately equals to Rs 487.
Since the down payment is Nil, the customer will pay EMI on Rs 24,360
As the rate of interest is Nil, the EMI paid will be calculated by solving the total cost by the total number of months.
\[\dfrac{{24360}}{{24}}{\text{ = Rs 1,015}}\]
We have to calculate the total amount paid including down payment, processing charge and amount paid as EMI in 24 months.
0 +487+24,360=Rs 28,907.
Hence, we can see that scheme 01 is the best among all other schemes.

Note: Many students forget to add processing charge while calculating the total amount of T.V. Also, for scheme 03, the total cost can be calculated by just adding the processing charge to the cost of the T.V. as the rate of interest and down payment is Nil in that particular case.