Simple Interest & Compound Interest & Surds & Indices

Simple interest

Short-term loans administered by financial institutions are typically subject to simple interest, calculated on a year-to-year basis. The same is true for the money that has been invested for a short period of time. There are two types of interest rates: simple interest rates and compounded interest rates.

SI Formula –

S.I. = Principal × Rate × Time

Compound interest

Interest accrued on the principal and interest accrued over some time is known as compound interest. Compound interest (CI) is also known as “interest on interest” because of this. Loan and investment rates are heavily dependent on this factor.

CI Formula –

C.I. = Principal (1 + Rate)Time − Principal

Surds and Indices

• Surds

A surd is the irrational square root of a whole number. An index number is a number raised to a multiple of a power. The index tells how many times the number is multiplied by itself.

• This type of surd is known as a simple surd when there is only one number in the root symbol. 

• Pure Surd: Irrational surds are known as pure surds. Surds are said to be similar if they share the same common characteristics.

• Mixed Surds: A mixed surd is a number that can be expressed as the product of rational and irrational digits.

• Compound surds are created by multiplying or dividing two or more simple surds.

• A binomial surd is formed when two surds are combined into one.

• Indices

Index numbers are numbers that have been multiplied by a factor. It tells you how many times you have to multiply the number by itself, which is called the index or power.

Quantitative Aptitude is one of the important sections in competitive examinations.

Let us see the important questions of simple and compound interest amplitude questions.

Simple and compound interest questions

• The difference between simple interest and compound interest on a certain sum of money in two years at 10% p.a. Is Rs.50. Does the total sum come to?

a) Rs. 1000

b) Rs. 6567

c) Rs. 5000

d) Rs. 2800

e) None of these

Answer: C 

Explanation : Given that the Difference between SI & CI for 2 years is Rs. 50, 

then Principal = x (100/r)² P = 50 x (100×100)/(10×10) → 

P = 5000.

• When a certain amount of money is invested for two years at the same interest rate, the compound interest of Rs. 208 and the simple interest of Rs. 200 are very different. Determine the corresponding percentage.

a) 5 %

b) 26 %

c) 71%

d) 23%

e) 8 %

Answer : E

Explanation : SI = Rs. 200 = Rs. 100 + Rs. 100

CI = Rs. 208 = Rs. 100 + Rs. 108 (In first year SI & CI are equal.)

Therefore, Rs.8 Gap is because of the 1st year interest.

Rs. 8 is interest on Rs. 100, R= (8×100)/(100×1) % ,R = 8%

Indices question

Here are some of the important Indices questions.

• (2a/b)2x-4 = (b/2a)2x-4 find value of x.

a) 2

b) 4

c) 6

d) 8

Answer: A

Explanation : 

(2a/b)2x-4 = (b/2a)2x-4

(2a/b)2x-4 = (2a/b)-2x+4

⇒ 2x – 4 = -2x + 4

⇒ 4x = 4 + 4

⇒ 4x = 8

⇒ x = 2

• If 17x = 4913, find the value of 22x-1.

a) 16

b) 32

c) 64

d) 128

Answer : B

Explanation : 17x = 4913

⇒17x = 4913

⇒17x = (17)3

⇒x = 3

Value of 22x-1 

⇒ 22.3-1

⇒ 25 = 32

Simplifying surds

Surds can be simplified by making sure the number under the root sign (this number is called the radicand) does not have any square numbers as a factor in it. Extracting square factors from the root sign reduces the number as much as possible.

Conclusion

The formula for calculating simple interest is S.I. = P. R.T, where P stands for the principal, R represents the annual percentage rate of interest, and T represents the time in years. The interest rate is expressed as r/100 and is expressed as a percentage.

Compound interest is calculated on the sum of the principal and interest that has been accrued. It is calculated using the following formula: C.I.= P × (1+r)2 – P

A number that has been raised to a higher power is an index number. It tells you how many times you have to multiply the number by itself, called the index or power.

A surd is the irrational square root of a whole number. An index number is a number raised to a multiple of a power. The index tells how many times the number is multiplied by itself.