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SI-CI
If you are preparing for any bank/railways exam, you must have come across straightforward and compound interest questions. Here we will see what SI-CI is, with si and ci difference, formulas, and other ci and si in 3 years. You will also be seeing some examples for better understanding.
What is Simple Interest?
When you invest your money in any bank, the bank provides you with interest on your investment. The banks apply various types of interests. One of them is simple interest. Simple interest is the easy and quick method to calculate interest on money. In simple interest, interest always applies to the original principal amount, with the fixed interest rate for every time cycle in a loan. A loan is an agreement between a bank or financial authority and a person who borrows money from them to fulfill their needs in exchange for a mortgage.
What is Compound Interest?
Compound interest, also known as compounding interest, is the interest on a loan or deposit calculated based on the initial principal amount and the accumulated interest from previous periods. Compound interest can be thought of as “interest on interest,” and will make a sum grow at a much faster rate. Think about compound interest as what happens in the “snowball effect.” A snowball starts small, as the principal amount does. But the more snow that’s added, the bigger it gets, just like interest added to the principal amount. As it grows, its size increases faster, just like the total amount at the end of every period.
SI CI Formula
Simple Interest Formula
The formula for calculating simple interest is simple and easy. One of its forms is →
Simple Interest=P×I×N
where:
P=Principal
I=Interest rate
N=Number of days between payments.
Simple interest is also calculated with the formula below:
S.I. = P × R × T,
where P = Principal,
R = Rate of Interest in % per annum, and
T = Time, generally in years.
The interest rate is in percentage r% and is to be written as r/100.
Principal: The principal is the amount initially borrowed from the bank or invested. The principal is denoted by P.
Rate: Rate is the percentage of interest at the principal amount given to someone for a particular time. The interest rate can be 5%, 8%, or 12%, etc. The rate of interest is denoted by R.
Time: Time is the duration generally in years for which the loan is given to someone. Time is denoted by T.
Amount: the total amount a person needs to return to the bank. It includes the principal amount and interest on it.
Amount = Principal amount + Simple Interest
A = P + SI
A = P + PRT
A = P(1+RT)
Compound Interest Formula
You can compute the compound interest with the help of the formula mentioned below:
A = P(1+r/n)nt
To use this calculation, one must know the variables below:
A: The total amount you would deal with at the end.
P: The principal amount.
r: The annual interest rate, written in decimal format. Which could be 5%, 8%, or 15%…
n: the number of compounding periods per year. For example, the compounding period monthly is 12, and weekly is 52.
t: the amount of time generally in years, through which money is compounded.
Difference between SI CI
The major difference between compound and simple interest is very simple and clear. Simple interest is based on the principal amount or a loan only, whereas Compound Interest is based on the principal amount as well as the interest that accumulates in every period of time.
Simple Interest | Compound Interest |
In Simple interest, interest for all years is the same for whatever number of years the loan continues. | In compound interest, interest for all years is different. Its rate of increase in interest accelerates over time. |
Sl is much smaller than Cl | Cl is comparatively larger than SI |
Formula is PxRxT/100 | Formula is: A = P(1+R/100)nt |
Interest is on Principal amount only. | Interests on previous interest as well as the principal amount. |
2-year CI SI difference formula
The difference between compound and simple interest for two years is given by the following formula:
Difference = P(R)2/(100)2
Here, P = principal amount,
R = rate of interest
3-year CI SI difference formula
The difference between compound and simple interest for three years is given by the following formula:
Difference = 3xP(R)2/(100)2 + P(R/100)3
Here, P = principal amount,
R = rate of interest
Examples
Example1. A student obtains a simple-interest loan to pay one year of college fee, which costs $18,000, and the rate of 6% annual interest. The student wants to repay the loan in three years. What would be the amount of simple interest he would have to pay?
Solution→
Simple Interest= P*I*T
$3,240 = $18,000 × 0.06 × 3
⇒ $3,240
and the total amount to be paid is
$18,000 + $3,240 = $21,240
Example2. If an amount of $5,000 is deposited into a savings account. The annual interest rate is 5%, which is compounded monthly. What would be the value of the investment after 10 years?
Solution→
Given,
P = 5000.
r = 5/100 = 0.05 (decimal).
n = 12.
t = 10.
If we put the given values in the formula, we get,
A = 5000(1 + 0.05/12)(12*10) = 8235.05
∴ The investment balance after 10 years at the rate of 12% interest would be $8,235.05.
Example3. The difference between the compound and simple interest on a particular sum at the rate of 12% per annum for two years is Rs. 90. What will be the value of the amount at the end of 3 years if it is compounded annually?
Solution→
Difference = P(R)2/1002
after putting the values into the equation, we get,
90 = P(12)2/(100)2
90*1002/122 = P
P = Rs. 6250.00
Calculating the compound interest on Rs. 6250 would be,
A = 6250(1 + 12/100)3
A = 6250(112/100)3 = 6250(1.12)3
A = 8780.20
The compounded total amount after three years would be Rs. 8780.80
Conclusion
In this article we have tried to make the student’s understand the simple interest and compound interest. We discussed their definitions, formulas, differences and examples. Hope this article gives a good insight about simple interest and compound interest.
