Quant(Concepts): Simple Interest

Quant(Concepts): Simple Interest

The basic formula for calculating simple interest is:

(Principal × Rate × Time) / 100.

Since for a particular time a fixed rate of interest is applicable on a fixed principal, so the interest received for every year is constant.

For Example:

If rate of 10% p.a. is applicable on Rs. 1000 principal, the interest is Rs. 100 for every year. In short, it can be stated that the total interest as a percentage of principal, is a multiple of time and rate as principal is constant, i.e. interest on Rs. 1000 invested for 4 years @ 12.5% p.a. is same as 50% (12.5 × 4) on Rs. 1000 which is Rs. 500. Thus, it can be concluded that total interest as a percentage of principal can be converted to a percentage question by multiplying rate and time before hand and calculating an effective rate of interest per annum.

Example 1:

Amount: Rs. 3750; Rate: 6.25%; Time: 4 years; Principal: ?

Solution:

As 6.25 × 4 = 25%. Now this question has effectively been converted into a number questions, with a number being increased by 25%.

Hence, the original number or the principal is  3750/1.25 = 3000.

Example 2:

Amount after 5 years = 6000 and Amount after 3 years = 5500. Find the Principal and Rate %.

Solution:

It can be seen that in 2 years Rs. 500 is added (as simple interest remains same for every year) or Rs. 250 is added every year.

Now, 5500 is the amount in which 3 years interest is added which is 250 × 3 = 750.

So, Principal = 5500 – 750 = 4750.

Rate % = 250/4750 × 100 = 5.25% approx.

Example 3:

A sum doubles itself in 4 years. It will take how many years to become 8 times?

Solution:

Rs. 100 becomes Rs. 200 in 4 years, so Rs.100 is the interest earned in 4 years. Hence every year Rs. 25 is earned, which makes the rate as 25%.

Now you need to make Rs. 100 as Rs. 800 in order to become 8 times, which requires Rs. 700 as total interest.As 25 is received every year, so 700 is received in 700/25 = 28 years.