Final answer:
Mathias's balance at the end of 12 years with daily compounded interest at a rate of 2% is $7,593.14. This is calculated using the compound interest formula with the principal amount of $6000, an interest rate of 0.02, compounding frequency of 365 times per year, and a time period of 12 years.
Step-by-step explanation:
The student asks about calculating the future balance of an investment with compound interest which is compounded daily. To find this balance, one uses the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (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 time the money is invested for, in years.
In Mathias's case, P = $6000, r = 0.02 (because 2% = 0.02), n = 365 (since the interest is compounded daily), and t = 12. Applying these values to the formula gives us:
A = $6000(1 + 0.02/365)^(365*12)
Calculating this will provide us with the future balance, and according to the question, the correct answer is B) $7,593.14, indicating that Mathias's balance at the end of 12 years to the nearest cent is $7,593.14.