## Focus Topic: Simple Interest (Arithmetic/Commercial Mathematics)

## CAT Simple Interest Installments Questions: An important concept for the topic

One concept that you should most definitely look into in an in-depth manner is the concept of CAT Simple Interest Installments. Installements is actually a part of both simple and compound interest. Let’s explore what this is concept is all about.

**What is an installment?**

Well, we all know that at times we don’t have enough money to buy something say a car. That doesn’t stops us from buying it. So, what do we do? We agree to pay the dealer a certain money at the end of a certain time period (this time period may be monthly or yearly). These partial payments which we pay after certain time intervals are called installments.

But is this so simple? Is there any benefit to us or to dealer? Why dealer agrees to receive money in parts rather than the whole money?

But is this so simple? Is there any benefit to us or to dealer? Why dealer agrees to receive money in parts rather than the whole money?

The dealer in this case earns interest on the money he has effectively lent to us. The installments decided in this case consist of two components, which is the principal amount and the interest amount.

Let’s take up a couple of tricky problems to understand how CAT Simple Interest Installments questions work.

**Question:** A tennis racquet worth Rs. 700 was bought by paying a down payment of Rs.100 and 6 equal installments of Rs. 100 each. Calculate the rate of interest.

- 300/7
- 400/7
- 56
- 300/11

**Solution: **

As the amount has to be paid in 6 equal installments, the payment on principal to be made will end on the completion of 6 months. He will have to pay (600/6=Rs.100 per month)

Principal for the first month will be 600, for second month=500, for third month=400 and so on.

Total sum or principal= 600+500+400+300+200+100=2100

Amount= Principal + interest= 600+100=700 (for one month)

Rate = 100* interest/ principal * time

Rate= (100*100)/(2100*1/12)=400/7 %

Hence, option (b)

**Question:** What annual installment will discharge a loan of Rs. 1025 due in 2 yrs @ 5% per annum?

- 200
- 300
- 400
- 500

**Solution: **

Let the installment be equal= x

At the end of the first year, the amount paid will be = 1.05x

At the end of the second year, the amount paid will be= x

Total amount paid is = 2.05x

This is equal to Rs. 1025.

Therefore,

2.05x=1025

x=500

Hence, option (d)

The complete concept notes for this topic are provided in the link below. Kindly read the full concept article to understand the topic.

**Simple Interest: Concepts and Exercises**

**Interest and Installment **

**Interest and Installment Exercise **

*Simple Interest: Topic Tests*

**Simple Interest Test-5**

** Simple Interest Test-6**

**Additional Mathematics Resources:**

**Arithmetic Level-wise Test: Level-1 Test-7**

** Basic Maths: Test-7**

**Logical Reasoning and Data Interpretation: Prep Resources**

**Data Interpretation: DI Level-1: Set 7**

** Logical Reasoning: LR Level-1: Set 7**

** Puzzle: Puzzle-7**

**CAT Question a Day**

What annual installment will discharge an amount of Rs 5760 due in 6 years if the rate of simple interest is 8% per annum?

a. Rs. 740

b. Rs. 810

c. Rs. 800

d. Rs. 850

### Answer and Explanation

**Answer: (c)**

Let each installment is of Rs 100

The first installment will be paid one year from now i.e. 5 years before it is actually due.

The second installment will be paid two years from now i.e. 4 years before it is actually due.

The third installment will be paid 3 years before it is actually due.

The fourth installment will be paid 2year before it is actually due.

The fifth installment will be paid 1 year before it is actually due.

The sixth installment will be paid on the day the amount is actually due.

So, on the first installment, the interest will be paid for 5 years, on the second for 4 years, on the third for 3 years, on the fourth for 2 years, on the fifth for 1 year and on sixth for 0 years.

In total, an interest for 15 years will be paid (5 + 4 + 3 + 2 + 1 + 0) on Rs 100 @ 8 %.

Interest = {(100 x15x8)/100} = Rs. 120 and the principal is Rs 100 × 6 = Rs. 600.

The total loan that can be discharged is Rs 600 + 120 = Rs 720

Now for Rs 720 the installment required is Rs. 100,

for Rs. 5760 the installment = (100/720) x 5760 = Rs. 800

Thanks for the free prep.