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In this exercise, assume that there are no deposits or withdrawals. An initial deposit of $1,000 earns 13% interest, compounded monthly. How much will be in the account in 5(1)/(2) years?

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Final answer:

For an initial deposit of $1,000 earning 13% interest compounded monthly over 5.5 years, the future value of the account would be $1964.47.

Step-by-step explanation:

To calculate the future value of an initial deposit receiving compounded interest, you can use 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, and t is the time the money is invested for in years.

For an initial deposit of $1,000 earning 13% interest, compounded monthly, over 5(1)/(2) years, we would substitute P = 1000, r = 0.13, n = 12, and t = 5.5 into the formula.

So, the calculation is as follows:

A = 1000(1 + \frac{0.13}{12})^{(12)(5.5)}

A = 1000(1 + 0.0108333)^{66}

A = 1000(1.0108333)^{66}

A = 1000(1.964473)

A = $1964.47

Thus, after 5(1)/(2) years, the amount in the account would be $1964.47.

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