# Simple Interest

**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.**