Final answer:
The function for the amount to which a $63,000 investment at 4 1/2% interest compounded quarterly grows after t years is A(t) = 63000(1 + 0.045/4)^(4t).
Step-by-step explanation:
To find the function for the amount to which the investment grows after t years with an initial investment of $63,000 at 4 1/2% interest compounded quarterly, we use the compound interest formula:
A(t) = P(1 + \frac{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).
- 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.
Given:
- P = $63,000
- r = 4.5% or 0.045 (as a decimal)
- n = 4 (since interest is compounded quarterly)
We substitute these values into the formula:
A(t) = 63000(1 + \frac{0.045}{4})^{4t}
This function can be used to calculate the future value of the $63,000 investment at any time t years in the future.