In this article we are going to be about Simple Interest and Compound Interest. It covers the important topics like Simple Interest and Compound Interest and Simple Interest vs Compound Interest.
Simple Interest:
In Mathematics, Simple Interest is a quick and easy method of calculating the interest charge on a given amount of money or loan.
We can determine this by Simple Interest multiplying the daily rate of interest by the principal by the number of days (n) that elapse between payments.
The formula for Simple Interest is ,
Simple Interest (SI) = \[\frac{(P\times R\times T)}{100}\]
Where, P is equal to the Principal, R is the equal to the Rate of Interest, T = Time (Period).
The time is in years and the rate of interest is in percentage (%).
NOTE :
Simple interest is calculated by multiplying the rate of interest by the principal and by the number of days (time period) that elapse between the payments.
It benefits consumers who pay their loans on time or early every month.
Auto loans and short-term personal loans are examples of places where Simple Interest is used.
We can calculate the total amount, using the following formula:
Amount = Principal + Interest
Where, Amount (A) is equal to the total money paid back at the end of the time period (T) for which the money was borrowed.
Compound Interest:
Compound interest is defined as the interest calculated on the principal and the interest accumulated over the previous period of time.
Compound interest is different from the Simple Interest.
In Simple Interest the interest is not added to the principal while calculating the interest during the next period while in Compound Interest the interest is added to the principal to calculate the interest.
The formula for Compound Interest is ,
Compound Interest (CI) = \[Principal \left ( 1+\frac{Rate}{100} \right )^{n}-Principal\]
where, P is equal to principal , R is equal to rate of Interest, T is equal to Time (Period)
The Formula to Calculate the Amount is
\[Amount=Principal \left ( 1+\frac{Rate}{100} \right )^{n}\]
where , P is equal to Principal , Rate is equal to Rate of Interest, n is equal to the time (Period).
Applications of Compound Interest:
Some of the applications of Compound Interest are:
Increase in population or decrease in population.
Growth of bacteria.
Rise in the value of an item.
Depreciation in the value of an item.
What is the Difference Between Simple Interest and Compound Interest?
Besides Simple Interest there is another type of interest known as Compound Interest.
The major difference between Compound and Simple Interest is that Simple Interest is based on the principal of a deposit or a loan whereas Compound Interest is based on the principal and interest that accumulates in every period of time.
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Here’s the Difference Between Simple Interest and Compound Interest in a Tabular Form(SI vs CI)
Simple Interest | Compound Interest |
The Simple Interest is the same for all the years. | The Compound Interest is different for all the years. |
SI < CI. | CI > SI. |
Simple Interest (SI) = (P×R×T)/100 | CI = Principal (1+Rate/100)n - principal |
Relation Between Simple Interest and Compound Interest -
Here’s the relation between Simple Interest and Compound Interest:
We already know from the SI vs CI definition that the interest is typically expressed as a percentage, and can be Simple or Compound Interest. Simple interest is generally based on the principal amount of a loan or deposit whereas Compound Interest is based on the principal amount and also on the interest that accumulates on the principal every period. We have already discussed this in the SI vs CI definition.
Questions to be solved:
1. Sohan takes a loan of Rs 1000 from the Central bank for a period of one year. The given rate of interest is 10% per annum. Find the interest and the amount Sohan has to pay at the end of one year.
Ans: Let’s write down the given information,
Here, the loan amount = Principal = Rs 1000
Rate of interest = R = 10%
Time for which it is borrowed = T = 1 year
The formula to calculate the Simple Interest for one year,
Simple Interest (SI) = \[\frac{(P\times R\times T)}{100}\]
Thus, the Simple Interest for a year, (SI) = \[\frac{(P\times R\times T)}{100} = \frac{(1000\times 10\times 1)}{100}\]
Now, let’s calculate the amount of money at the end of one year,
Amount = Principal + Interest
The amount that Sohan has to pay to the bank at the end of one year = Principal + Interest = 1000 + 100 = Rs 1100.
2. Ram borrowed a sum of Rs 5000 for 2 years at the rate of 3% per annum. Find the interest accumulated on the sum of at the end of 2 years and calculate the total amount.
Ans: Let’s write down the given information,
P = Rs 5000
R = 3%
T = 2 years
The formula to calculate the Simple Interest for one year,
Simple Interest (SI) = \[\frac{(P\times R\times T)}{100}\]
(SI) = \[\frac{(P\times R\times T)}{100} = (SI) = \frac{(5000\times 3\times 2)}{100} = Rs. 300\]
Now, let’s calculate the amount of money at the end of two years,
Amount = Principal + Interest
The amount that Ram has to pay to the bank at the end of two years = Principal + Interest = 5000 + 300 = Rs 5300.
3. Mahi pays Rs 5000 as an amount on the sum of Rs 2000 which he had borrowed for 3 years. What is the rate of interest?
Ans: Let’s write down the given information,
Amount at the end of three years = Rs 5000
Principal= Rs 2000
SI = Amount – Principal = 5000 – 2000 = Rs 3000
Time = 3 years
Rate =?
We know the formula to calculate the Simple Interest,
(SI) = \[\frac{(P\times R\times T)}{100}\]
R = (Simple Interest × 100) /(Principal× Time)
R = (3000 × 100 /5000 × 3) =0.2%
Thus, R = 0.2%
4. The count of a certain breed of bacteria was found to increase at the rate of 5% per hour. What will be the growth of bacteria at the end of 3 hours if the count was initially 6000.
Ans:
Since the population of bacteria increases at the rate of 5% per hour,
We know the formula for calculating the amount,
\[Amount=Principal \left ( 1+\frac{Rate}{100} \right )^{n}\]
Thus, the population at the end of 3 hours = 6000(1 + 3/100)3
= 6000(1 + 0.03)3 = 6000(1.03)3 = Rs 6556.36.
The essential differentiation between Simple Interest and Compound Interest is that Simple Interest is determined on the chief sum alone, while Compound Interest is determined on the chief sum in addition to intrigue accumulated over a period cycle.
We as a whole realize that Simple Interest and Compound Interest are two key ideas that are every now and again utilized in different monetary administrations, especially in banking. Straightforward interest is utilized in advances, for example, portion advances, car credits, understudy loans, and home loans. The Compound Interest is utilized by most of the bank accounts to pay the premium. It pays something beyond interest. Allow us to have at the distinction between Simple Interest and Compound Interest inside and out in this post.
Straightforward and Compound Interest definitions
Straightforward Interest: Simple premium is characterized as the chief measure of an advance or store made into an individual's ledger.
Build Interest: Simply put, Compound Interest will be interest that amasses and accumulates over the chief sum.
What is the Simple Interest equation?
Basic premium is determined by duplicating the period's financing cost by the chief sum and the residency. The term may be estimated in days, months, or a long time. Accordingly, the loan fee should be deciphered prior to being increased by the chief sum and residency.
To process Simple Interest, utilize the accompanying equation:
Straightforward Interest = P*I*N
Where
P signifies the chief sum.
I – The time frame's loan cost
N represents residency.
What precisely is Compound Interest?
Build revenue (CI) acquires revenue on the recently procured revenue, rather than Simple Interest, which acquires interest on the primary total. The interest is applied to the head. CI represents Interest on Interest. The entire idea depends on creating critical returns by building interest on the primary sum.
As such, CI can possibly yield a better yield than essentially procuring revenue on a venture. Since Compound Interest depends on the essential force of accumulating, ventures rise dramatically.
The recurrence of compounding is dictated by the bank, monetary organization, or moneylender. It tends to be done on an every day, month to month, quarterly, half-yearly, or yearly premise. The higher the recurrence of accumulating, the more prominent how much premium gathered. Subsequently, financial backers benefit more from Compound Interest than debt holders.
Build revenue is utilized by banks for certain credits. Accumulate revenue, then again, is most regularly used in contributing. Accumulate revenue is likewise utilized by fixed stores, shared assets, and whatever other speculation that considers benefit reinvestment.
What is the Compound Interest Formula?
CI is determined by increasing the chief sum by one or more the interest to the force of the accumulating time frames. At last, the essential sum should be eliminated to compute the CI.
To register Compound Interest, utilize the accompanying equation:
A =\[ P \left ( 1+\frac{r}{n} \right )^{nt}-1\]
Where
A = Annual Percentage Yield
P signifies the chief sum.
What is the Significance of Compounding?
Accumulating is a circ*mstance wherein premium procures interest. Basically, it demonstrates that when profit are reinvested, both the underlying speculation and the reinvested income ascend at a similar speed. This makes the ventures develop at a higher rate. This is alluded to as the force of compounding. The higher the intensifying recurrence, the better the venture returns. The occasions interest is accumulated in an entire year is alluded to as the building recurrence.
Compounding is an interesting thought, and it's nothing unexpected that Albert Einstein named it the "Eighth Wonder of the World." Compounding permits you to make your cash turn out more enthusiastically for you. Over the long haul, collecting revenue acquires a higher interest. Furthermore, the more extended measure of time you stay contributed, the greater the profit from the venture. Accordingly, it is ideal to start contributing early on to benefit from the force of compounding.
