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In the above compound interest formula, the time is in fractions; therefore the rate of the return can be calculated by subtracting the amount from the principal. The annual compound interest calculation depends on the time and the fraction of the time determines the rate of return on yearly basis. The fraction time is calculated by dividing the rate of the interest by 4 to determine the amount quarterly. Time in fraction changes time for calculating the average return on the investment.
What is the formula for Annual compound Interest?
C.I. = (A−P)
=P (1+rn) nt−P
=P [(1+rn) nt−1]
In the above formula P is denoted as the principal, A is adopted as the amount, r is denoted as the rate of interest and n is denoted as the number of times interest is compounded and t is denoted as the time for the investment. The annual compound rate can be calculated in a fraction of the time also where the rate of the return is divided by a fraction of the time in the investment. Annual compound interest is calculated by multiplying the initial investment with 1 plus the annual interest rate collected in the compound time minus one.
A brief description of compound interest annually
Compound interest annually gets the return on both the initial principal and the interest generated in the unit time of the compound period. The calculation of the compound interest depends on the time and annual interest rate compounded in the unit time. It is essential to know the value of the three quantities in the annual compound interest calculation to determine the value of the 4th quantity in the equation. Compound interest annually is calculated by the below formula:
P [(1 + i)n – 1]
In the above equation, n is denoted as the unit time and is denoted as the annual interest rate in the invested amount.
What is the formula for compound annual growth rate?
The compound annual growth rate value is calculated by dividing the investment value at the end of the period by the value at the beginning of the period. The compound annual growth rate gives the result of one exponent by dividing the number of the period. The formula is presented below:
CAGR= (EV/BV) 1/n-1×100
In the above equation, EV is denoted as the ending value and BV is denoted as the beginning value. Moreover, n is denoted as the number of periods in the CAGR rate calculation. The CAGR rate is not the true return on the annual compound interest as the value is changing due to the period of time.
Explain a time in a fraction in annual compound interest
Let the amount of principal is P, the Rate of interest is R and the time period is 17/4, then the calculator of the annual compound interest can be done by the below formula:
Amount= P [1+R/100]3 * [1+5/4*R/100]
Therefore the amount of the compound interest in the fraction time depends on the value of R and the change of the return can change the value of the compound interest in fraction time.
The function of time in the compound interest annually
Time is directly proportional to the rate of the return in the compound interest annually or in fraction time. In a fraction of time, the return of the investment depends on the initial principal amount of investment and the interest generated in the unit rate of the compound time. The fraction of time is multiplied by the value of the principle to determine the amounts of return in a fixed rate of annual interest. It is essential to know the value of the annual interest rate and amount to calculate the value of the unit fraction time in the compound interest.
Properties of annual compound interest in the fraction time
Annual compound interest in fraction time is denoted by the below equation and it is calculated by multiplying the fraction by the rate of the interest.
A= P (1+R/100) t
Here if the time is in fractions, then it is multiplied by the function of time in the compound interest calculation. The annual compound interest depends on the value of the unit time and the rate of interest in the unit time. If time is in fraction then the rate of return depends on both the principal and the interest generated in the compound time.
Conclusion
The above study indicates that CAGR is the growth rate where the annual average rate of return is calculated by the above formula. Compound interest is the fraction of time that determines the importance of the rate of interest in the given period. The time in that the amount is invested can change the return of the investment. The above study illustrates that it is necessary to determine the time fraction to calculate the value of the return.
