Calculating Compound Interest for a 12% Annual Rate Compounded Semi-Annually on $2500 for One Year
Compound interest is a powerful concept in finance, allowing an initial investment to grow significantly over time. In this article, we will illustrated how to calculate the compound interest on an investment of $2500 for one year at an annual interest rate of 12%, compounded semi-annually. We will use the compound interest formula to determine the final amount and the compound interest earned.
The Compound Interest Formula
The formula for compound interest is given by:
Formula Breakdown
[ A P left(1 frac{r}{n}right)^{nt} ]
Where:
A is the amount of money accumulated after n years, including interest. P is the principal amount, or the initial amount of money. r is the annual interest rate (decimal). n is the number of times that interest is compounded per year. t is the number of years the money is invested or borrowed for.Applying the Formula
In our specific scenario:
P $2500 (the principal amount) r 12% 0.12 (annual interest rate) n 2 (since it is compounded semi-annually) t 1 (one year)Step-by-Step Calculation
Substitute the values into the formula: [ A 2500 left(1 frac{0.12}{2}right)^{2 times 1} ] Calculate (frac{0.12}{2} 0.06): [ A 2500 left(1 0.06right)^{2} ] This simplifies to: [ A 2500 left(1.06right)^{2} ] Calculate (1.06^{2} 1.1236): [ A 2500 times 1.1236 2809 ] Therefore, the final accumulated amount is $2809.Calculating the Compound Interest Earned
To find the compound interest earned, subtract the principal from the total amount:
Compound Interest Calculation
[ text{Compound Interest} A - P 2809 - 2500 309 ]
Thus, the compound interest earned on the initial investment of $2500 for one year at 12% compounded semi-annually is $309.
Conclusion
This thorough illustration shows how to calculate compound interest for a $2500 investment at 12% annual interest, compounded twice a year. This type of calculation is fundamental in understanding how investments grow over time and can be applied to a variety of financial contexts. Whether for personal investments or business planning, a clear grasp of compound interest is essential.