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if you deposit 2,000 in an account that pas 6.5% annual interest compounded semi-annually what is the balance after three years?

User GisMofx
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Final answer:

You would calculate the balance after three years by applying the compound interest formula to the initial deposit of $2,000 with an annual rate of 6.5% compounded semi-annually, resulting in a total amount of $2,436.80.

Step-by-step explanation:

If you deposit $2,000 in an account that pays 6.5% annual interest compounded semi-annually, the balance after three years can be calculated using the compound interest formula:

A = P(1 + \frac{r}{n})^{nt}
Where:

  • A is the amount of money accumulated after n 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.

Plugging the values into the formula, we get:

A = $2,000(1 + \frac{0.065}{2})^{2\times3}
A = $2,000(1 + 0.0325)^{6}

A = $2,000(1.0325)^{6}

A = $2,000\times1.218402

A = $2,436.80

The balance in the account after three years will be $2,436.80.

User Michael Dillon
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