Simple Interest

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The topic of consideration in this article is Simple Interest. But before we begin with “simple interest”, let us define the term interest.

Interest is actually one of the most fundamental business terms, and without it, the financial trading of the world would come to standstill. Interest is defined as the “time value of money”. What exactly does this mean? Well, look at this way: with time, the value of money changes. Suppose you Rs. 100 in the year 2000. Would it still be Rs. 100 or would the amount have grown? If you had deposited the money in a saving bank account, say with an annual rate of interest 4%, that money would have definitely grown by now. Can you calculate the amount you would have with you in 2013? Well, in case you can’t right now, go through these concept notes and you would know the answer.

The concept of simple and compound interest is especially applicable to the world of banking and economics. Whenever we borrow a certain sum of money (known as the principal), we pay back the original amount accompanied with a certain amount of interest on that amount. In a way, those are the charges of borrowing that sum of money. Simple interest is one method of determining the amount due at the end of a loan duration. Another method of interest application is compound interest, but we study about it in the next article.Simple Interest Tooltip 1: The Definitions

Principal (P): The original sum of money loaned/deposited. Also known as capital.
Interest (I): The amount of money that you pay to borrow money or the amount of money that you earn on a deposit.
Time (T): The duration for which the money is borrowed.
Rate of Interest (R): The percent of interest that you pay for money borrowed, or earn for money deposited.

Simple Interest Tooltip 2: The Formula

Simple Interest (SI) = (P x R x T)/100

Where:
P: Principal (original amount)
R: Rate of Interest (in %)
T: Time period (yearly, half-yearly etc.)

Amount Due at the end of the time period, A = P (original amount) + SI
A = P + { (P x R x T)/100 }

If you have a close look, Simple Interest is nothing else but an application of the concept of percentages.

Simple Interest Tooltip 3: Basic Problems to explain the concept

Basic Problem 1: What is the SI on Rs. 7500/- at the rate of 12% per annum for 8 years?
Using the Basic Formula:
Simple Interest (SI) = (P x R x T)/100
P – Principal amount, T- Number of years, R – Rate of Interest
Given P = 7500, N = 8 Years, R = 12%
S.I = (7500X12X8)/100
S.I = 7200

Basic Problem 2: A man borrowed rs.15000/- at the rate of 24% SI and to clear the debt after 6 years, much he has to return:
Using the Basic Formula:
Simple Interest (SI) = (P x R x T)/100
P – Principal amount, T- Number of years, R – Rate of Interest
Given P = 15000, T = 6 Years, R = 8%
S.I = PNR / 100
S.I =(15000X24X6)/100
= 21600
Therefore, total interest = 21600
Total repayment = S.I + Principal amount
Answer = 21600 + 15000 = Rs 36600

Basic Problem 3: A man borrowed Rs.12000 at the rate of 10% SI, and lent the same sum to another person at the rate of 15% what will be the gain after 5 years?
Using the Basic Formula:
Simple Interest (SI) = (P x R x T)/100
P – Principal amount, T- Number of years, R – Rate of Interest
A man borrowed at 15%
He lent the same sum to another person at 15%
Therefore his gain is actually equal to the different in the interest rate (per year) 15 – 10 =5% for 1 year
Thus, to calculate his gain, we use this difference as the rate of interest.
Given T = 5 years and P = Rs. 12000
First we are calculating for Rs. 100
Amount Gained = (12000x5x5)/100 = Rs. 3000
Therefore his gain = Rs. 3000/-

Simple Interest Tooltip 4: Understanding Simple Interest Through Solved Multiple Choice Examples

Example 1: A sum of money at simple interest amounts to Rs. 850 in 3 years and to Rs. 900 in 4 years. The sum is:

A.Rs. 650 B.Rs. 690 C.Rs. 698 D.Rs. 700

Answer: Option D
Explanation:
S.I. for 1 year = Rs. (900 – 850) = Rs. 50
S.I. for 3 years = Rs.(39 x 3) = Rs. 150
Original Amount/ Principal = Rs. (850 – 150) = Rs. 700

Example 2: Maninder invested into two different schemes, P and Q at simple interest rate of invested an amount of Rs. 15,000. Rate of interest for scheme P & Q were 14% p.a. and 18% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 5000, what was the amount invested in Scheme P?

A.Rs. 5000 B.Rs. 6500 C.Rs. 7200 D.Rs. 7500

Answer: Option A
Explanation:
Let the sum invested in Scheme P be Rs. x and that in Scheme Q be Rs. (15000 – x).
Then,
{x x 14 x 2}/100 + {(15000 – x) x 18 x 2}/100 = 5000
28x+540000-36x=500000
8x=40000
x=5000
Hence, money deposited in scheme x = 5000.

Example 3: A sum of Rs. 15,000 amounts to Rs. 19,500 in 5 years at the rate of simple interest. What is the rate of interest?

A.3% B.4% C.5% D.6%

Explanation:
S.I. = Rs. (19500 – 15000) = Rs. 4500.
We know:
Simple Interest (SI) = (P x R x T)/100
P – Principal amount, T- Number of years, R – Rate of Interest
Therefore,
4500 = (15000xRx5)/100
R = 6%

Example 4: How much time will it take for an amount of Rs. 900 to yield Rs. 81 as interest at 2.25% per annum of simple interest?

A. 3 years B. 4 years C. 5 years D.6 years

Explanation:
We know:
Simple Interest (SI) = (P x R x T)/100
P – Principal amount, T- Number of years, R – Rate of Interest
Therefore:
81 = (900×2.25xT)/100
T = 4 years

Example 5: A money-lender claims he lends money at simple rate of interest of 10% per annum. But he cleverly tricks the farmers by including the interest amount in the principal when he calculates it every six months. The effective annual rate of interest he is charging is:

A.10% B.10.25% C.10.5% D. 10.75%

Explanation:

Let the sum be Rs. 100. Then,
S.I. for first six months = Rs. (100 x 10 x 1)/(100×2)
= Rs. 5
Increase principal for the last six months= Rs. 105
SI for the last six months = Rs. (105 x 10 x 1)/ (100×2)
SI = Rs. 5.25
Net interest charged in an year = Rs. 10.25
Hence, effective rate of interest = (10.25/100) x 100 = 10.25%.