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Lauren deposited $19,000 today. He plans to withdraw $1200 every year. For how long can she withdraw from the account starting 1 year from now if interest is 5.1% compounded annually?

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Final answer:

Lauren can withdraw from the account for approximately 30 years starting 1 year from now.

Step-by-step explanation:

To find out how long Lauren can withdraw from the account, we need to calculate the future value of the initial deposit of $19,000. We can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the future value, P is the principal (initial deposit), r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, the initial deposit is $19,000, the interest rate is 5.1%, compounded annually, and the annual withdrawal is $1,200. Let's solve for t:

$19,000 = $1,200 * (1 + 0.051/1)^(1t)

Dividing both sides by $1,200 gives:

15.83 = (1.051)^t

Taking the logarithm of both sides, we get:

t = log(15.83) / log(1.051)

Using a calculator, we find that t ≈ 29.95. Therefore, Lauren can withdraw from the account for approximately 30 years starting 1 year from now.

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