**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. youâ€™ll pay Rs. 200000 and take the car.

But what if you donâ€™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**

There are two types of problems asked from this concept.

**Type 1:**

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.

**Example:** A device is available for Rs 5000 cash or Rs 500 down payment followed by 4 equal installments. If the rate of interest charged is 25% per annum simple interest, calculate the monthly installment.

**Solution:**Â After paying a down payment of 500 amount to be paid will be

5000-500=4500

Total amount of installments for 4 months will be

Now let us discuss the next type of questions which are often confused with previous type.

**Type 2:**

**Example:** What annual installment will discharge a debt of Rs 770 due in 5 years, the rate of interest being 5% per annum?

**Solution:**Installment paid at the end of 1^{st}, 2^{nd}, 3^{rd}, 4^{th} and 5^{th}year will be simple interest paid for 4,3,2,1,0years respectively .

Let us suppose the installment given is 100rs

At the end of the first year amount paid will be => 100 + {(5x4x100)/100} = Rs. 120

At the end of the second year amount paid will be =>100 + {(5x3x100)/100} = Rs. 115

At the end of the third year amount paid will be =>100 + {(5x2x100)/100}= Rs 110

At the end of the fourth year amount paid will be =>100 + {(5x1x100)/100}= Rs 105

At the end of the fifth year amount paid will be= Rs 100

Total amount paid is = 120+115+110+105+100= Rs 550

For an amount of Rs 550 annual installment is Rs100

For Rs 770 it will be =(100 x 770)/550 = RS. 140

**Shortcut Formula**

The annual payment discharged while paying a debt of Rs. A due in n years at the rate of interest r% per annum is

**Example 2:** What annual installment will discharge a loan of Rs. 832 due in 2 yrs @ 8%pa?

**Solution:**

If Principal = x

x+1.08x= 2.08x=832

x=400

Using the formula, annual installment= [{(100 x 832)/(100×2)+(8x2x1)}] = 400

**Type 3: **

**Example:** A mobile worth Rs. 500 can be bought by paying a down payment of Rs.100 and 8 equal installments of Rs. 50 each. Calculate the rate of interest.

**Solution: **

As it has to be paid in 8 equal installments, the payment on principal to be made will end on the completion of 8 months. He will have to pay (400/8=Rs.50 per month)

Principal for the first month will be 400, for second month=350, for third month=300 and so on.

Total sum or principal=400+350+300+250+200+150+100+50=1800.

Amount= Principal + interest= 400+50=450 (for one month)

Rate = 100* interest/ principal * time

Rate= (100*50)/(1800*1/12)=100/3 %

### Installments paid with Compound Interest

To calculate the installments paid with compound interest, we use the following formula:

Where,

P= Principal

R=rate

n= number of installments

x= Amount of installment

**Example: **A sum of Rs. 1275 is borrowed at 4% pa compound interest and paid back in 2 equal annual installments. What is the amount of each installment?

**Solution:**

Let the value of installment be x

Equating the amounts

1275x(1.04)2=x +1.04x

x= Rs. 676

**Example:** A sum of Rs. 550 is to be repaid in 2 equal annual installments. If rate =20% compounded annually, then the value of each installment will be?

**Solution:**

Let the value of installment be x

Equating the amounts

550*(1.2)^{2}=x+1.20x

x= Rs. 360

**Example:** Three equal installments, each of Rs. 300, were paid at the end of the year on a sum borrowed at 20% compounded annually. Find the sum.

**Solution:**

Rate= 20%

Installment = Rs.300

Principal=?

Putting these values in the formula:

### Simple Interest (Complete Lesson): Table of Contents

**Concept Articles****Exercise **

**Practice Tests **