**When Interest is Compounded Annually but Time is in Fraction**

Compound interest, which is compounding annually but the time is fractional, means that the rate of interest varies each year; compound interest is more beneficial.

Compound interest is such a typical interest method, which is calculated based on the interest of previous years. This kind of method is known as the “interest on interest” process. Mathematically, simple interest is easier to calculate and fruitful for the borrowers. This assignment is based on compound interest. which is calculated annually, but the required time interval is fractional. It means that any individual will get different rates of interest on their investment in different years.

**Simple & Compound interest **

As per the method of simple interest, it is based on the total amount of principal of any loan or fixed deposit. However, taking any personal loan can get more benefits as per the strategy of simple interest. Simple interest is such a typical method, in which the money creditors will have to only pay the interest rather than any extra charges. Also for the money borrowers, this method is very fruitful, because they do not have to pay any charge based on interest from previous years. There are various advantages of simple interest and those advantages are such as the Simple interest method is set for a certain amount of time frame and also for a significant amount. The most important part of this method is the money borrowers will not have to pay any significant amount on the interests of previous years. The loans based on simple interest can be paid early. The standard formula of the simple interest is = P*I*N, where P refers to the total principal amount,’ I’ refers to the daily rate of interest and the N refers to the required time intervals. The simple interest method is simpler than the compound interest but it is more beneficial to get large interest.

Compound interest is a distinguished method where the interest amount is calculated not only based on the total principal amount but also it is estimated based on the interest in previous years. That’s why this interesting method is known as the “interest on interest”. As per the strategy of compound interest, money investors are highly benefited through this process as it helps to grow the fund or wealth faster rather than the simple interest method. The standard formula of the compound interest is CI= [P(1+i/n) nt – P], where CI stands for the interest of previous years, P stands for the total amount of principal, and n stands for the frequency of compounding amount per year, i is the rate of interest, and t is the time period. Compound interest has various strategies, sometimes, the amount is compounded annually, sometimes quarterly basis, and sometimes annually compounding method is followed for different fractional times in different years. However, it can be said that the simple interest method is easier to calculate and also helpful for taking any personal loan. Though the compound interest method has more complexities than the simple interest, it is ultimately fruitful for the investors as it increases the future values for reinvesting the money.

**When Interest is Compounded Annually but Time is in Fraction**

As per the method of compound interest, the amount is compounded based on the principal amount and the interest of previous years. Annually compound interest means the principal amount is compounded twice in a whole year. However, the annual compound interest is more fruitful for the money investors rather than the simple interest method. In the case of the compound interest method where there is a fractional period, it helps to grow the money or the funds more quickly rather than the normal annual compounding method. However, in the case of the fractional annual compounding method, the rate of interest is varied in different years and that’s why there is a high chance of increasing the principal amount and the investors can further reinvest the higher values of interest. The continuous compounding method helps to increase the principal amount faster rather than the fractionally annual compounding method.

**Conclusion **

From doing the over assignment based on simple and compound interest, it can be said that both of the strategies are beneficial for specific individual purposes. As per the strategy of simple interest, the borrowers do not have to pay an amount based on previous interest. However, this kind of method is suitable for any personal loan or auto loan. Whereas, compound interest helps to grow any fund at a faster rate. But the annual compounded interest is less fruitful than the continuous compounding as the investors can instantly get their interest within a regular period.