Final answer:
To calculate the number of years it will take for an account to reach $14,300, you can use the formula for compound interest. Let's say the initial amount is $10,000 and the interest rate is 5% (0.05) compounded annually. Plugging these values into the formula, it will take approximately 9.22 years for the account to reach $14,300.
Step-by-step explanation:
To calculate the number of years it will take for an account to reach $14,300, we need to know the initial amount and the interest rate. Assuming there is no additional contribution or withdrawal made, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount ($14,300 in this case)
P is the principal amount (initial amount)
r is the annual interest rate (expressed as a decimal)
n is the number of times interest is compounded per year
t is the number of years
Let's say the initial amount is $10,000 and the interest rate is 5% (0.05) compounded annually. Plugging these values into the formula:
$14,300 = $10,000(1 + 0.05/1)^(1t)
Simplifying the equation:
1.43 = (1.05)^t
Taking the logarithm of both sides:
log(1.43) = log((1.05)^t)
Using logarithm properties, we can bring the exponent down:
log(1.43) = t * log(1.05)
Solving for t:
t = log(1.43) / log(1.05)
Using a calculator, the approximate value of t is 9.22 years. Rounding to the nearest hundredth, it will take approximately 9.22 years for the account to reach $14,300.