Aptitude Simple And Compound Interest Problems

Simple And Compound Interest Problems

Type 1: Simple Interest Formula Based Direct Problems. (Easy But They Can Be Twisted. See Why)

You will find this type to the easiest of all the 4 types we are going to discuss here. In this type, you will be applying the direct simple interest formula.

Here is your familiar simple interest formula
SI = PNR/ 100

The four variables in the above formula are : 

SI = Simple Interest

P = Principal Amount (This the amount invested)

N = Number of years 

R = Rate of interest (per year) in percentage

Note: Amount A you will get by investing an amount P for N number of years at R percent rate per annum will be
 

A = SI +P

Can they be twisted? Yes. See Why

A questioner can give you all values for the variables except one variable. For example, the questioner may give you SI, P and R and ask you to find N. But, nowadays these type of simple questions are hard to find. This type can be twisted with so many variations but the basics is still the same. Below example question is a slightly twisted version.

You will understand this type clearly after reading the below example:..

Example Question 1: A certain sum of money amounts to Rs.2000 in 2 years and to Rs.2500 in 3 years. Find the sum and rate of interest.

Solution:
Let P be the amount invested.

You know that the amount becomes 2000 in 2 years and 2500 in 3 years. You can see that the amount increases by Rs. 500 between 2nd and 3rd years.

Therefore, you can easily say that the simple interest for 1 year = 2500 – 2000 = 500

So, simple interest for 2 years = 500 x 2 = 1000

From the question, you know that the amount A after 2 years = 2000

Now using the formula A = P + SI,

you can write P = A – SI = 2000 – 1000 = 1000

Now, you know P = Rs.1000, N = 2 years and Simple interest SI = Rs.1000.

If you substitute above values in the formula SI = PNR / 100, you will get R as shown below:

R = (100 x 1000) / (1000 x 2)

R = 50%

Therefore, the sum invested P = 1000 and rate of interest R = 50%.

 

Type 2. Compound Interest Formula Based Direct Problems. (Are They Similar To Type 1?)

In this type, you will be getting problems dealing directly with the below compound interest formula.
 

CI = [P(1 + R/100)N] – P

The variables in the above formula are as follows:

CI = Compound Interest

P = Principal (Amount invested)

R = Rate of interest in percentage per year

N = Number of years

Note: There is a special case when the interest is compounded (calculated and added to the amount invested) half yearly instead of yearly basis. In that case, CI formula becomes
 

half yearly CI = [P(1 + (R/2)/100)2n] – P

Like type 1 (simple interest), this type can be twisted. But here we are going to see a straightforward example.

Example Question 2: Find compound interest on Rs.6000 at 12% per annum for 2 years compounded annually.

Solution:
From the question, you know that N = 2 years, R = 12%,P = Rs.6000

If you substitute the above values in the formula CI = [P(1 + R/100)n] – P, you will get

CI = [6000(1 + 12/100)2] – 6000

= (6000 x 28/25 x 28/25) – 6000

= 7526.40 – 6000

= Rs.1526.40

 

Type 3: Difference Between Compound And Simple Interests

This type is based o the difference between simple and compound interests. For example, in the below example, you will be given the difference between SI and CI and you have to calculate principal:

Example Question 3: The difference between the compound interest and simple interest on a certain sum at 12% per annum for 2 years is Rs.700. Find the sum.

Solution:
You have to start by assuming principal to be X.

From the question, you know that N = 2 years, R = 12%

Case 1: Let us start with Compound Interest:

You have to apply P = X, N = 2 and R = 12 in compound interest formula as shown below:

CI = [P(1 + R/100)n] – P

= (X[1 + 12/100]2) – X

= (X[112/100]2) – X

= (X[28/25 x 28/25] ) – X

CI = 159X / 625 …. equation 1

Case 2: Now let us move on to Simple Interest

Now you have to substitute P = X, N = 2 and R = 12 in simple interest formula.

SI = PNR/100

= (X x 2 x 12) / 100

= 24X/100 

SI = 12X/50 … equation 2

Case 3: Now let us find P

You know from the question that the difference between simple and compound interests is 700
Therefore,

CI – SI = 700 (We are writing CI first because CI will be higher than SI same rate of interest and same number of years)

If you substitute CI and SI values from equations 1 and 2, you will get

159X/625 – 12X/50 = 700

(318X – 300X)/1250 = 700

18X/1250 = 700

700 x 1250 = 18X

Or, X = 48611.11

Therefore, Principal (Sum invested) = Rs.48611.11

 

Type 4: Direct Problems With Both SI And CI (How Type 3 Is Different From Types 1 and 2?)

This type is a combined type of types 1 and 2. In this type, you have to apply both simple and compound interest formulas according to the question.

You will understand this after reading the below example.

Example Question 4: If the simple interest on a sum of money at 6% per annum for 4 years is Rs.1600, then find the compound interest on the same sum for the same period at the same rate.

Solution:
From the question, you know that R = 6%, N = 4 years, SI = Rs.1600

If you apply the above values in the simple interest formula SI = PNR/100, you will get

1600 = P x 4 x 6 / 100

Or P = (1600 x 100) / 6 x 4

P = 6333.33

Using the above value of P, you have to now calculate CI as shown below: 

CI = [P(1 + R/100)n] – P

= [6333.33(1 + 6/100)4] – 6333.33

= [6333.33 (106/100)4] – 6333.33

= [6333.33 x 53/50 x 53/50 x 53/50 x 53/50] – 6333.33

= 7995.68 – 6333.33
= Rs.1662.35