Final answer:
The function y(t) represents the total balance after t years in the form y(t) = 500(1 + 0.048/12)^12t. After 8 years, using the formula and the given annual interest rate compounding monthly, the balance would be approximately $740.12.
Step-by-step explanation:
To answer the first part of the question, we need to write a function y(t) that represents the total balance after t years with an annual interest rate of 4.8% compounded monthly. The formula provided seems to have a typo as it lacks the rate in the parentheses. The correct formula for compound interest would be:
y = P(1 + r/n)nt
Where:
- P is the principal amount (initial investment).
- r is the annual interest rate (decimal).
- n is the number of times interest is compounded per year.
- t is the number of years the money is invested for.
To express this with the given data:
y(t) = 500(1 + 0.048/12)12
For the second part, to find the balance after 8 years, we substitute t with 8
y(8) = 500(1 + 0.048/12)12*8
Now, calculate the balance:
y(8) = 500(1 + 0.004)96
y(8) ≈ 500(1.004)96
y(8) ≈ 500 * 1.48024275
y(8) ≈ $740.12
Therefore, the balance after 8 years would be approximately $740.12.