Concept of Installment

Suppose you have to buy a car at Rs. 200000. You can pay the seller in two ways: Either you can pay the entire amount in one go i.e. you’ll pay Rs. 200000 and take the car.
But what if you don’t have enough money at the time of purchase?
The other option is that you pay some down-payment and give the remaining amount in the form of equal installments at regular intervals.

Note: In installment scheme the buyer pays more because in addition to installment a buyer has to pay an interest on it monthly or yearly.

What is Down payment?

It is the amount that is paid initially while buying the article. Rest is paid in form of installment and an interest on it.

Installments Paid With Simple Interest

If the total loan is taken for 4 months, then situation will be something like this:-
At the end of first month: Interest for next 3 months will be paid
At the end of second month: Interest for next 2 months will be paid
At the end of third month: Interest for next 1 month will be paid
At the end of Forth month: No Interest will be paid
So, if x denotes installment variable, R for rate % per annum, t for time, then every month
Amount to be paid= x + amount of interest
The table will look like this.

This amount will be equal to the principal borrowed and interest given on that for 4 months.

Question 1:A watch is sold for Rs.440 cash or for Rs.200 cash down payment together with Rs.244 to be paid after one month. Find the rate of interest charged in the installment scheme.

a. 10%                                   b. 15%                                   c. 20%                                   d. 25%

Solution:

Principal for the next month = 440 - 200 = 240
Amount paid after next month = 244
Therefore interest charged at Rs.244-240=4
(240 x R x 1)/(12x100)=4
R=20%
Rate of interest (R) = 20% per annum

Question 2:. A cell phone is available for Rs. 600 or for Rs.300 cash down payment together with Rs.360 to be paid after two months. Find the rate of interest charged under this scheme.

a. 20%                                   b. 50%                                   c. 120%                                 d. None

Solution:

Principal for the next month = 600-300=300
Amount paid after two month = 360
Therefore interest charged at Rs.360-300=60
(300 x R x 2)/(12x100)=60
R=120%
Rate of interest (R) = 120% per annum

Question 3: . Samsung mobile phone is available for Rs.2500 cash or Rs.520 cash down payments followed by 4 equal installments. If the rate of interest charged is 25% per annum Simple interest, calculate the monthly installment

a. 520                                    b. 480                                    c. 550                                     d. None of these

Solution:

Principal for the next month = 2500-520=1980
Number of Installmenment=4

Rate=25%

x=[1980(1+(4x25)/(12x100)]/ [4+(4x3)/2 x25/12x1/100]=520

So instalment=520

Question 4:  Kishore purchases a track suit for Rs.2400 cash or for Rs.1000 cash down payments and two monthly installments of Rs.800 each. Find the rate of interest.

a. 75%                                   b. 120%                                                c. 50%                                   d. None of these

Solution:

Principle for first month=2400-1000=1400
Principle for second month=1400-800=600
Total pronciple for 2 month=2000
Interest=1600-1400=200
SI=PxRxT/100
2000xR/12x1/100=200
R=120%

Question 5:. What annual installment will discharge a debt of Rs 2,360 due in four years at 12% p.a. simple interest?

a. 400                                    b. 500                                    c. 300                                     d. 600

Solution:

Installments paid at the end of 1st, 2nd, 3rd and 4th years earn a simple interest at 12% p.a. for 3, 2, 1 and 0 years respectively.
Hence the respective installments amount to, (100 + 3 x 12), (100 + 2 x 12), (100 + 1 x 12) and 100, when annual installment is Rs 100.
Hence amount paid is Rs. 136 + Rs 124 + Rs 112 + Rs 100 i.e., Rs 472, when the annual installment is Rs.100
For an amount of Rs 2,360, annual installment = 2,360×100/472=Rs.500