Simple Interest

Simple Interest is an easy method of calculating the interest for a loan/principal amount. Simple interest is a concept which is used in most of the sectors such as banking, finance, automobile, and so on. when you make a payment for a loan, first it goes to the monthly interest and the remaining goes towards the principal amount. In this article, let us discuss the definition, simple interest formula, and how to calculate the simple interest with examples.

What is Simple Interest?

Simple Interest (S.I) is the method of calculating the interest amount for some principal amount of money. 

Simple interest formula is given as:

SI = (P × R ×T) / 100

Where SI = simple interest

P = principal

R = interest rate (in percentage)

T = time duration (in years)

In order to calculate the total amount, the following formula is used:

Amount (A) = Principal (P) + Interest (I)

Now let us solve some examples to get acquainted with these formulae.

Question 1: Find the simple interest on Rs. 68,000 at 16(2/3)% per annum for a period of 9 months?

A) Rs. 8500                  B) Rs. 3200                 C) Rs. 2100                 D) Rs. 4300

Solution:

Here, P = Rs. 68000, R = 50/3% per annum and T = 9/12 years = 3/4 years.
Note that the time has been converted into years as the rate is per annum.
The units of rate R and the time T have to be consistent. Now using the formula for the simple interest, we have:

S.I. = [{P×R×T}/100];
S.I. = Rs. [68000×(50/3)×(3/4)×(1/100)] = Rs. 8500.
Thus the correct option is A

Question 2:  Khan borrows some money at the rate of 6% p.a. for the first two years. He borrows the money at the rate of 9% p.a. for the next three years, and at the rate of 14% per annum for the period beyond five years. If he pays a total interest of Rs. 11400 at the end of nine years, how much money did he borrow?

A) Rs. 12000               B) Rs. 21000                 C) Rs. 37000                 D) Rs. 63000

Solution:

 Let ‘x’ be the sum that Khan borrows. Then the total simple interest that Khan pays is the sum of the interests.

We can write from the formula of the simple interest, [x×6×2]/100 + [x×9×3]/100 + [x×14×4]/100 = Rs. 11400.

Therefore we can write, 95x/100 = 11400 or x = Rs. 12000 and hence the correct option is A) Rs. 12000.

Question 3: The simple interest on a certain sum of money for 2(1/2) years at 12% per annum is Rs. 40 less than the simple interest on the same sum for 3(1/2) years at 10% per annum. Find the sum.

A) Rs. 600                    B) Rs. 666                C) Rs. 780                D) Rs. 800

Solution: Let the sum be Rs. a. Then we can write: [{x×10×7}/{100×2}] – [{x×12×5}/{100×2}] = 40.. This can be written as: 7x/20 – 3x/10 = 40.  Therefore we have x = Rs. 800

Hence the sum is Rs. 800 and the correct option is D) Rs. 800.

Question 4:: A man took a loan from a bank at the rate of 12 % p.a. simple interest. After three years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was:

A) Rs. 12000                 B) Rs. 11000                    C) Rs. 14000                         D) Rs. 15000

Solution:

Here we have, the principal = Rs. [{100×5400}/{12×3}] = Rs. 15000. Thus the correct option is D) Rs. 15000.

Question 5:: Khan invests a certain amount in three different schemes A, B and C with the rate of interest 10% p.a., 12% p.a. and 15% p.a. respectively. If the total interest that accumulates in one year was Rs. 3200 and the amount he invests in scheme C was 150% of the amount he invests in Scheme A and 240% of the amount he invests in Scheme B, what was the amount he invests in scheme B?

A) Rs. 4000                B) Rs. 5000                C) Rs. 6000                        D) Rs. 7000

Solution: Let x, y and z be the amounts that Khan invests in schemes A, B and C respectively.
Then, we can write using the formula for S.I., : [{x×10×1}/100] + [{y×12×1}/100] + [{z×15×1}/100] = Rs. 3200.
Also, we have the conditions that 10x + 12y + 15z = Rs. 320000.

Now, we have z = 240% of y = (12/5)y. And, z = 150% of x = (3/2)x
or in other words we can write:

x = (2/3)z = [(2/3)×(12/5)]y = (8/5)y.

Combining the above equations, we have:

16y + 12y + 36y = Rs. 320000 or in other words, we can write 64y = Rs. 320000 and y = Rs. 5000.

Therefore the sum that Khan invests in scheme B = Rs. 5000 and the correct option is B) Rs. 5000.