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Assume 5000 dollars is invested into an account with a interest rate if 5.0 percent compounded monthly find a formula for the amount A(t) in the account after t years

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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.

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