Final answer:
It will take approximately 29.169 years for the account to be worth $750.
Step-by-step explanation:
To find out how long it will take for the savings account to be worth $750, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
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- A is the final amount in the savings account ($750)
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- P is the initial deposit ($500)
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- r is the annual interest rate (5.6% expressed as 0.056)
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- n is the number of times the interest is compounded per year (quarterly, so n = 4)
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- t is the number of years
Plugging in these values, we get:
$750 = $500(1 + 0.056/4)^(4t)
Simplifying this equation, we have:
1.5 = (1.014)^t
To solve for t, we take the natural logarithm of both sides:
ln(1.5) = t * ln(1.014)
Using a calculator, we find that ln(1.5) ≈ 0.4055 and ln(1.014) ≈ 0.0139.
Therefore, t ≈ 0.4055 / 0.0139 ≈ 29.169 years.
So, it will take approximately 29.169 years for the account to be worth $750.