Compound Interest Formula

In practice, simple interest is rarely employed; practically all banks or other financial organizations use compound interest. When interest is added (or compounded) to the principal sum, interest is paid on the entire amount. If the first year’s interest is left there in the account, and the interest again for the second year is computed on the total amount accrued thus far.

Compound interest rates accelerate the growth of money. This allows the amount of money to grow at a faster rate than simple interest because the individual receives a return on the same capital he has invested and a return at the end of each compound period. That means they no longer have to make big money to realize their ambitions.

When it comes to accumulating assets, the magic of composition can be very beneficial. The previous method was to create a stock option and start saving money. The more money you save, the more money you get through compound interest. It is also crucial for mitigating monetary factors such as rising living costs, falling costs, and loss of purchasing power.

COMPOUND INTEREST CALCULATION METHOD

So the formula of compound interest is 

and where N denotes the number of periods.

If the compound interest rate varies from year to year, then

COMPOUND INTEREST CALCULATION FOR DIFFERENT YEARS

The formula is often referred to as the periodic compounding formula.

Here,

• A is the new principal sum or amount of income after the compounding period
• P denotes the original or starting amount
• The yearly interest rate is denoted by r
• The compounding frequency, or how often interest is repeated in a year, is represented by N
• The number t denotes the number of years

And the statistics show that the compound interest rate during the first year is very much like the simple interest rate. (Pr)/100.

Except during the first year, yearly compounded interest is always larger than simple interest.

Practise question

QUESTION 1: Rock lends $4000 to stone at a 10% annual interest rate, compounded semi-annually over two years.  Determine how much money he receives from stone after two years?

Answer: The principal amount “P” is $ 4,000. The interest rate “r” is 10% per year. Conversion period = half a year, interest for half a year = 10/2% = 5%. The time period “t” is 2 years. The compound frequency ‘n’ is 2. We will replace the provided data with the compound interest formula:

That final amount is $ 4,862.03 and the compound interest formula makes the solution simple.

FORMULA OF INTEREST FOR DIFFERENT PERIODS

• In the situation in which the principal amount is compounded monthly, the following formula is used to compute compound interest:

The compound interest for a month is computed here (period) thus, the interest rate r is divided by 12 as well as the period is repeated 12 times.

• Daily compounded formula

The everyday compound interest formula calculates interest 365 times each year, which is why the value of n is 365. The daily compound interest formula, according to the explanation, is as follows:

is the compound interest formula where interest is compounded daily.

• When interest is calculated quarterly, it is referred to as compound interest. Because one year has four quarters, the rate of interest will be one-fourth of the annual rate, and the time period will be four times the duration specified in years.

As a result, with quarterly interest amount is calculated as