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Bùi Quang Tín đang tìm kiếm từ khóa What is the formula for difference between simple interest and compound interest for 3 years? được Cập Nhật vào lúc : 2022-10-15 00:50:28 . Với phương châm chia sẻ Mẹo về trong nội dung bài viết một cách Chi Tiết 2022. Nếu sau khi Read Post vẫn ko hiểu thì hoàn toàn có thể lại Comments ở cuối bài để Ad lý giải và hướng dẫn lại nha.Rs. 5,00,000Rs. 6,00,000Rs. 3,00,000Rs. 4,00,000 Nội dung chính
- Answer (Detailed Solution Below)Simple Interest:NOTE : Compound Interest:The Formula to Calculate the Amount isApplications of Compound Interest:What is the Difference Between Simple Interest and Compound Interest?Here’s the
Difference Between Simple Interest and Compound Interest in a Tabular Form(SI vs CI)Relation Between Simple Interest and Compound Interest -Questions to be solved:What is the difference between compound interest and simple interest for 3 years a rate of interest 10% per annum for Rs 1000?What is the difference between compound interest and simple interest for 4 years?What is the formula of difference between SI and CI for 2 years?How do you find the difference between simple and compound interest?
Answer (Detailed Solution Below)
Option 1 : Rs. 5,00,000
Shortcut Trick
CI effective rate for 3 years 5% p.a = 15.7625%
SI effective rate for 3 years 5% p.a = 15%
Rate difference = (15.7625 - 15)% = .7625%
⇒ P = (3812.5/.7625) × 100
⇒ P = 5,00,000
∴ The required sum is Rs. 5,00,000.
Given:
CI - SI difference for 3 years = Rs. 3812.5
Rate = 5%
Time = 3 years
Formula used:
CI - SI = P(R/100)2 × [(300 + R)/100]
Calculation:
CI - SI = P(R/100)2 × [(300 + R)/100]
⇒ 3812.5 = P(5/100)2 × [(300 + 5)/100]
⇒ 3812.5 = P(25/10000) × (305/100)
⇒ P = (3812.5) × (10000/25) × (100/305)
⇒ P = 5,00,000
∴ The required sum is Rs. 5,00,000.
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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(Ptimes Rtimes 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 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+fracRate100 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+fracRate100 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 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(Ptimes Rtimes T)100]
Thus, the Simple Interest for a year, (SI) = [frac(Ptimes Rtimes T)100 = frac(1000times 10times 1)100]
Now, let’s calculate the amount of money the end of one year,
Amount = Principal + Interest
The amount that Sohan has to pay to the bank the end of one year = Principal + Interest = 1000 + 100 = Rs 1100.
2. Ram borrowed a sum of Rs 5000 for 2 years the rate of 3% per annum. Find the interest accumulated on the sum of 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(Ptimes Rtimes T)100]
(SI) = [frac(Ptimes Rtimes T)100 = (SI) = frac(5000times 3times 2)100 = Rs. 300]
Now, let’s calculate the amount of money the end of two years,
Amount = Principal + Interest
The amount that Ram has to pay to the bank 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 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(Ptimes Rtimes 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 the rate of 5% per hour. What will be the growth of bacteria the end of 3 hours if the count was initially 6000.
Ans:
Since the population of bacteria increases the rate of 5% per hour,
We know the formula for calculating the amount,
[Amount=Principal left ( 1+fracRate100 right )^n]
Thus, the population 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 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+fracrn right )^nt-1]
Where
A = Annual Percentage Yield
P signifies the chief sum.
What is the Significance of Compounding?
Accumulating is a circumstance wherein premium procures interest. Basically, it demonstrates that when profit are reinvested, both the underlying speculation and the reinvested income ascend a similar speed. This makes the ventures develop 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.
What is the difference between compound interest and simple interest for 3 years a rate of interest 10% per annum for Rs 1000?
= ₹ (331- 300) = ₹ 31. Q.. By using the formula, find the amount and compound interest on: The difference between the compound interest and the simple interest on a certain sum for 3 years 10% per annum is Rs 93.What is the difference between compound interest and simple interest for 4 years?
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.What is the formula of difference between SI and CI for 2 years?
Hence, rate of interest compounded annually for 2 years is 5% Q.. The difference between S.I. and C.I. (compounded annually) on a sum of 64000 for 2 years is 1000.How do you find the difference between simple and compound interest?
What is the main difference between simple interest and compound interest? Simple interest is computed on the principal amount or loan amount whereas compound interest is computed based on the principal amount as well as the interest accumulated for a certain period or previous period. Tải thêm tài liệu liên quan đến nội dung bài viết What is the formula for difference between simple interest and compound interest for 3 years?