Final answer:
The compound interest formula is A = P(1 + r/n)^(nt), where A is the amount, P is the principal, r is the rate, n is the number of times interest is compounded per year, and t is the time in years. An example calculation is provided.
Step-by-step explanation:
The question you are asking relates to the calculation of compound interest, which is a concept in finance and mathematics. To find the compound interest, you first calculate the Future Value using the formula Future Value = Principal x (1 + interest rate)^{nt}, where 'nt' is the product of the number of times interest is compounded per year (n) and the time the money is invested or borrowed for (t). Then, subtract the Principal from the Future Value to get the compound interest. So, compound interest is essentially the amount by which the Future Value exceeds the Principal. The compound interest formula is given by A = P(1 + r/n)^(nt), where A is the amount, P is the principal, r is the rate, n is the number of times interest is compounded per year, and t is the time in years.
For example, if you have a principal amount of $1000, an interest rate of 5% per year, interest being compounded annually, and a time period of 3 years, you can calculate the compound interest as follows:
A = 1000(1 + 0.05/1)^(1*3) = $1157.63