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If $10,000 is invested at 6% annual interest compounded annually, how long would it take for the account balance to reach $20,000?

User Elysire
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Answer:

To determine how long it would take for the account balance to reach $20,000 with an initial investment of $10,000 and an annual interest rate of 6% compounded annually, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the final account balance

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

n = the number of times interest is compounded per year

t = the number of years

In this case, we have:

P = $10,000

A = $20,000

r = 6% or 0.06 (as a decimal)

n = 1 (compounded annually)

Plugging in the values, we have:

$20,000 = $10,000(1 + 0.06/1)^(1*t)

Simplifying the equation:

2 = (1 + 0.06)^t

Taking the natural logarithm of both sides:

ln(2) = ln((1 + 0.06)^t)

Using the logarithmic property, we can bring down the exponent:

ln(2) = t * ln(1 + 0.06)

Dividing both sides by ln(1 + 0.06):

t = ln(2) / ln(1 + 0.06)

Using a calculator, we can find:

t ≈ 11.896

Therefore, it would take approximately 11.896 years for the account balance to reach $20,000 with a $10,000 initial investment and a 6% annual interest rate compounded annually.

User MarkSkayff
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