Suppose we examine our bank statements, we
note that some interest is credited each year to the same principal amount. For
the same principal amount, this interest is different each year. The bank
charges compound interest, known as CI because the interest increases for
successive years. Since interest increases for successive years, it is not
simple interest. CI is a tool that allows one to determine price changes by
compounding every year, half-yearly, quarterly, etc.
Through the examples given based on real-life applications, one can also understand why compound interest yields more than simple interest. In contrast to simple interest, the compound interest formula is calculated based on both the principal and interest accumulated over some time. However, compound interest does not have the same impact on the principal as simple interest. Among the many popular uses of compound interest are in the banking and finance sector, as well as in other areas. It can be used for things like Increase or decrease in population, bacteria growth, or rise or decrease in the value of goods.
The formula for
To calculate compound interest, we need to
know the amount and principal. It is the difference between amount and
principal. To calculate compound interest, we can use the compound interest
formula, which is:
Interest = Amount – Principal
Here, Amount (A) = P (1+r/n) nt
In this, A = amount, P = principal, r =
rate of interest, n = number of times interest is compounded per year, t = time
As noted above, this is the general formula
for discovering how many times the principal will compound in a given year.
the annual compound interest method, this amount is as follows:
A= P (1+R/100)t
If the interest rate is compounded
annually, half-yearly, quarterly, monthly, daily, and so forth, the compound
interest rate formula can be expressed differently.
How to derive the
formula for compound interest?
We know that SI for one year is equal to CI
(compound interest when compounded annually). So we can use the simple interest
formula to calculate compound interest.
For example, let P be the principal amount,
n years be the period, and R be the interest rate
The principal amount will shift
after the first six months, for which the interest for the next six months will
be calculated on the amount after six months.
Compound interest is calculated
on a half-year basis. Using the general formula for compound interest, the
half-yearly rate is divided by two and the time is multiplied by two.
In this case, since interest is
compounded quarterly, the principal amount will change after the first three
months (first quarter) and the interest and charges for the next three months
(second quarter) will be based on the balance after the first three months.
Likewise, interest will be
calculated on the remaining balance after the first 6 months for the third
quarter and over the remaining balance after the first 9 months for the fourth
Simple interest can
be learned in the same way with the help of experts at Cuemath, which helps
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