Final answer:
Using the compound interest formula A = P(1 + r/n)^(nt), with Trevon's initial investment of $6,715 at a 7% interest rate compounded 3 times per year for 20 years, we can calculate the future balance of the retirement account.
Step-by-step explanation:
The question involves the concept of compound interest, which is a key topic in mathematics related to finance and investments. To calculate the future value of an investment with compound interest, the formula used is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (initial investment), r is the annual interest rate (in decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.
To answer the student's question regarding compound interest, we would use the values provided:
- Principal (P) = $6,715
- Annual interest rate (r) = 7% or 0.07
- Number of times compounded per year (n) = 3
- Time in years (t) = 20
By substituting these values into the compound interest formula, we can calculate the future value of Trevon's retirement account after 20 years:
A = 6715(1 + 0.07/3)^(3*20)
By calculating the values inside the parentheses first and then raising to the power of 60 (3 times per year for 20 years), we can find the amount accumulated in the account.