Simple Interest

When a person borrows some amount of money from another person or organisation (bank), then the person borrowing money (borrower) pays some extra money during repayment, that extra money during repayment is called interest.

For example, If A takes Rs. 50 from B and after using Rs. 50, A returns Rs. 55 to B, then A pays (55-50) i.e., Rs. 5 as interest.

Let us consider following definitions before proceeding exercise

Principal (P) : Principal is the money borrowed or deposited for a certain time.

Interest (I) : Extra money paid for using other's money is called interest.

Amount (A) : The sum of principal and interest is called amount.

Amount = Principal + Simple Interest

Rate of Interest (R) :  It is the rate at which the interest is changed on principal. It is always specified in percentage terms

Time (T) : The period, for which the money is borrowed or deposited, is called time.

Basic Formula Related to Simple Interest

Simple Interest (S.I.):

If the interest is calculated on the original principal for any length of time, then it is called simple interest.

Let Principal = P, Rate = R% per annum (p.a.) and Time = T years. Then

 (i). Simple Intereest = P x R x T 100

 (ii). Principal(P) = 100 x S.I. R x T

 (iii). Rate(R) = 100 x S.I. P x T

 (iv). Time(T) = 100 x S.I. P x R

TIPS on cracking Aptitude Questions on Simple Interest

Tip #1:Understand the formulae

1.    Amount to be repaid after N years if simple interest is applied = P + (P x N x R) = P (1 + N x R)

2.    Simple Interest = P x N x R

3.    Amount to be repaid after N years if interest is compounded = P [(1 + R)^N]

4.    Compound Interest = [P x (1 + R)^N] - P

Question: Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs.4000 for 2 years at 10% per annum. Calculate the principal placed on simple interest.

Solution:

Let the Principal be Rs. P

Then, SI = (P x R x T) = 0.24P

Given CI = 4000(1 + 0.1)2 – 4000 = 4000(1.21 – 1) =4000 x 0.21

According to the question,

0.24P = 2000 x 0.21

=>    P = 2000 x 0.21 / 0.24 = 2000 x 7 / 8 = Rs. 1750

Tip #2:If the interest rate is applied on a half-yearly, quarterly or monthly basis, the effective annual rate is calculated by compounding the interest

Question: What is the effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly?

Solution:

Let the Principal be Rs. P.

Now, the rate is 6% per annum but the interest has to be paid twice a year (i.e.) an interest of 3% is applied every 6 months.

Amount to be repaid after 1 year = P x 1.03 x 1.03 = 1.0609P

=> Effective Annual Rate of interest = 6.09%

TTip #3:Use logarithms to find the time when compound rates are applied

1.    log 2 = 0.301

2.    log 3 = 0.477

3.    log 4 = 0.602

4.    log 5 = 0.699

5.    log 6 = 0.778

6.    log 7 = 0.845

Question: At 3% annual interest compounded monthly, how long will it take to double your money?

Solution:

Let the number of months be n and the Principal be Rs. P.

Then, P(1 + 0.03)n = 2P

=>  (1 + 0.03)n = 2

=>    n log ( 1.03) = log 2

=>    n = log 2 / log 1.03 = 0.301 / 0.128 = 23.5

Thus. It’ll take 1 year and 11.5 months.