Consider an investment of $10,000 that offers an annual nominal interest rate of 8%, compounded at different frequencies. You are tasked with calculating the future value of this investment after 5 years under varying compounding frequencies - annually, semi-annually, and quarterly.

Using the future value formula for compound interest, which is given by:

$$ FV = PV imes (1 + rac{r}{n})^{nt} $$

where:

• $$ FV $$ = Future Value
• $$ PV $$ = Present Value (initial investment)
• $$ r $$ = annual nominal interest rate
• $$ n $$ = number of compounding periods per year
• $$ t $$ = number of years

Your task is to find the future value for each compounding frequency and identify which compounding frequency yields the highest future value.