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Leo invested $7000 into an account that has a 3.5% annual interest rate. What equation best describes this investment after t years?

1. [tex]A(t) = 7000(1.35)^t[/tex]
2. [tex]A(t) = 7000(0.965)^t[/tex]
3. [tex]A(t) = 7000(0.035)^t[/tex]
4. [tex]A(t) = 7000(1.035)^t[/tex]

Answer :

Final answer:

The correct equation for the investment after t years with a 3.5% annual interest rate is A(t) = 7000(1.035)^t, illustrating the principle of compound interest.

Explanation:

The equation that best describes the investment after t years, given a principal amount of $7000 and an annual interest rate of 3.5%, is found using the formula for compound interest. You start your principal amount ($7000) and multiply it by 1 plus the annual interest rate (expressed as a decimal), raised to the power of the number of years t. Therefore, the correct equation is:

A(t) = 7000(1.035)^t

This is because each year, the account balances increases by a factor of 1 plus the interest rate. So if the rate is 3.5%, you would add 1 to 0.035 (the decimal form of 3.5%), giving you 1.035. Then, raise this to the power of t to account for the number of years the money is invested. This is how compound interest works to increase the value of the investment over time.

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