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**Compound interest (CI) calculator** - formulas & solved example problems to calculate the total interest payable on a given principal sum at a certain rate of interest over a period of time with either one of monthly, quarterly, half-yearly or yearly compounding frequency, in different world currencies such as USD, GBP, AUD, JPY, INR, NZD, CHF, RMB etc.

This calculator can be used for the following purposes

1. to calculate how much CI payable based on the yearly compounding frequency.

2. to calculate how much compound interest payable based on the half-yearly compounding frequency.

3. to calculate how much CI payable on the quarterly compounding frequency.

4. to calculate how much compound interest payable based on the monthly compounding frequency.

Compound Interest often abbreviated as CI is the time value of money as interest very similar to *simple interest (SI)* but the interest earned on principal will be added to the principal after a certain unit of time (compounding period or frequency), from that moment on, the interest will be paid both on the principal and on the interest that has been added to it. We can say it simply in other words that the interest earns itself interest. The principal amount P, total period n in years, compounding period or frequency and the interest rate R in percentage are the major components of compound interest calculation.

The below compound interest formulas are used in this calculator in the context of time value of money to find the total interest payable on a principal sum at certain rate of interest over a period of time with either monthly, quarterly, half-yearly or yearly compounding period or frequency.

**Formula for Yearly Compounding**

This below yearly compounding formula is one of the few formulas used in this calculator to find the total compound interest payable based on the annual compounded period

**Formula for Half-yearly Compounding**

This below half-yearly compounding formula is one of the few formulas used in this calculator to find the total compound interest payable based on the semi-annual compounded period

**Formula for Quarterly Compounding**

This below quarterly compounding formula is one of the few formulas used in this calculator to find the total compound interest payable based on 3 months compounded period

**Formula for Monthly Compounding**

This below monthly compounding formula is one of the few formulas used in this calculator to find the total compound interest payable based on the monthly compounded period

**Elements of Compound Interest**

__Principal Sum__

It is a sum of money which is borrowed or lended or invested. In compound interest calculation, the Principal amount changes after every compounding period such as the principal amount and interest earned after the first unit of time becomes the principal for the second unit, the principal amount and interest earned after the second unit of time becomes the principal for third time and so on. After that certain period, the difference between the amount and the money borrowed is the compound interest.

__Total Time Period__

It is a time period to which the principal amount is borrowed or lended or invested at a certain rate of interest. At the end of this period the total amount comprises of principal and interest should be returned.

__Compounding Period or Frequency__

It is a certain period of time after which an interest earned on principal during that period added to the principal is called as Compounding Period.

__Interest Rate__

Interest Rate in percentage is the rate at which the money is borrowed or saved or lended or invested.

The below solved example problems for compound interest may used to understand how the values of Principal amount P, Rate of interest R, Time period n & componding frequency are being used in the monthly, quarterly, half-yearly or yearly compounding formulas to find the total interest payable.

__Example Problem 1:__

How much amount of compound interest payable on a principal sum of 10,000 USD at 9% rate of interest for the total period of 3 years with yearly compounding frequency or period?

__Solution:__

P = 10,000 USD on yearly compounding frequency

R = 9%

n = 3 Years

apply these above values in the below annual compound interest formula

CI_{yearly} = P [1 + (R/100)^{n}]

= 10000 x [1 + (9/100)^{3}]

= 2950.29

The total interest payable is 2950.29 USD

__Example Problem 2:__

How much amount of total interest payable on a principal sum of 20,000 USD at 7% rate of interest for the total period of 4 years with half-yearly compounding frequency or period?

__Solution:__

P = 20,000 USD on half-yearly compounding frequency

R = 7%

n = 4 Years

apply these above values in the below semi-annual compound interest formula

CI_{half-yearly} = P (1 + [(R/2)/100]^{2n})

= 20000 x (1 + [(7/2)/100]^{(2 x 4)}

= 6336.18

The total interest payable is 6336.18 USD

__Example Problem 3:__

How much amount of total interest payable on a principal sum of 15,000 USD at 6% rate of interest for the total period of 5 years with quarterly compounding frequency or period?

__Solution:__

P = 15,000 USD on quarterly compounding frequency

R = 6%

n = 5 Years

apply these above values in the below quarterly compound interest formula

CI_{quarterly} = P (1 + [(R/4)/100]^{4n})

= 15000 x (1 + [(6/4)/100]^{(4 x 5)}

= 5202.83

The total interest payable is 5202.83 USD

__Example Problem 4:__

How much amount of total interest payable on a principal sum of 25,000 USD at 5% rate of interest for the total period of 3 years with monthly compounding frequency or period?

__Solution:__

P = 15,000 USD on monthly compounding frequency

R = 5%

n = 3 Years

apply these above values in the below monthly compound interest formula

CI_{monthly} = P (1 + [(R/12)/100]^{12n})

= 25000 x (1 + [(5/12)/100]^{(12 x 3)}

= 4036.81

The total interest payable is 4036.81 USD

Compound interest is a very important interest calculation to determine the time value of money in many financial instruments. The above formula & solved examples may used to understand how to calculate compound interest for the different compounding frequencies, however, when it comes to online for quick calculations, this compound interest calculator may used to find the total interest payable & total amount payable in different currencies in the World.

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