Final answer:
The formula for the amount A(t) in an account after t years with an initial investment at compound interest is A(t) = P(1 + r/n)^(nt). For $5000 at a 5.0 percent rate compounded monthly, the formula is A(t) = 5000(1 + 0.05/12)^(12t).
Step-by-step explanation:
To find the formula for the amount A(t) in the account after t years with an initial principal P investing at an interest rate r compounded monthly, you would use the compound interest formula which is:
A(t) = P(1 + r/n)^(nt)
Where:
- 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 this particular case, since the initial investment is $5000, the annual interest rate is 5.0 percent (or 0.05 in decimal form), and the interest is compounded monthly (n = 12), the formula becomes:
A(t) = 5000(1 + 0.05/12)^(12t)
So, after t years, the amount A(t) can be calculated using the above formula.