Question

What is the key difference between simple interest and compound interest, and how does this difference affect the effectiveness of each?

Answer 1

Answer:

The simple interest is calculated only on the principal amount of a loan so it is relatively easier to calculate than the compound interest.

The compound interest is calculated on the principle amount plus the interest that the amount gets per compounding period up to the period of the loan. In other words, in compound interest we get, interest on interest.

This difference between the both, is the reason, we get more money in compound interest than simple one.

Let us take an example-

Suppose the principle is = $5000

r = 5% or 0.05

t = 5 years

Simple interest formula is :

$p\times r\times t$

=> $5000\times0.05\times5=1250$

So, total amount after 5 years will become = $5000+1250=6250$ dollars.

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Lets check for compound interest where the interest is compounded annually.

p = $5000

r = 5% or 0.05

t = 5 years

n = 1

Compound interest formula is :

$A=p(1+\frac{r}{n} )^{nt}$

$A=5000(1+\frac{0.05}{1} )^{5}$

=>$A=5000(1.05)^{5}$

A = $6381.40

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We can see that we are getting more money in compound interest than the simple interest, for the same amount and same time period.

Answer 2

The key difference between simple interest (SI) and compound interest (CI) is that SI is calculated only on principal amount while CI is on principal amount plus accumulated interest.

What is simple interest and compound interest?

Simple interest-

Simple interest is the amount charged on the principal amount with a fixed rate of interest for a time period. Simple interest calculated only on the principal amount.

The formula for the simple interest can be given as,

$I=\dfrac{P\times r\times t}{100}$

Here, (I) is the interest amount  on the principal amount of (P) with the rate of (r) in the time period of (t)

Compound interest-

Compound interest is the amount charged on the principal amount and the accumulated interest with a fixed rate of interest for a time period.

The formula for the final amount with the compound interest formula can be given as,

$A=P\left(1+\dfrac{r}{100}\right)^t$

Here, (A) is the final amount (principal plus interest amount) on the principal amount of (P) with the rate of (r) in the time period of (t).

For the same interest rate, time period and same principal amount the simple interest is less than the compound interest.

• This difference affect the effectiveness of simple interest as, we get less amount of interest, which is not good for investing the money.

• This difference affect the effectiveness of compound interest as, we get more amount of interest, which is not good for borrowing the money or loan.

Hence, the key difference between simple interest (SI) and compound interest (CI) is that SI is calculated only on principal amount while CI is on principal amount plus accumulated interest.

Learn more about the simple interest here;

https://brainly.com/question/2294792

Learn more about the compound interest here;

https://brainly.com/question/24274034