Final answer:
To model the account's value after t years with compound interest, use the function A(t) = $570(1.0128)^{4t}. The APY, calculated using the compound interest formula, is approximately 5.20% when compounded quarterly.
Step-by-step explanation:
To write a function showing the value of the account after t years with $570 invested at a 5.1% annual interest rate, compounded quarterly, we can use the compound interest formula: A(t) = P(1 + r/n)nt
Where: A(t) is the amount of money accumulated after t years, including interest.
P is the principal amount (the initial amount of money) which is $570.
r is the annual interest rate (decimal), so 5.1% is 0.051.
n is the number of times that interest is compounded per year, which is 4 for quarterly.
t is the time in years.
So, the function will be: A(t) = $570(1 + 0.051/4)4t
This simplifies to: A(t) = $570(1 + 0.01275)4t
For rounding the coefficients to four decimal places, we get: A(t) = $570(1.0128)4t
To find the annual percentage yield (APY), we use the formula: APY = (1 + r/n)n - 1
APY = (1 + 0.051/4)4 - 1
After calculating, rounding to the nearest hundredth of a percent:
APY ≈ 5.20%