Final answer:
To find the number of years it will take for Ashley's investment to reach a value of $16,000, use the formula for compound interest. It will take about 5.07 years for Ashley's investment to reach a value of $16,000, and about 8.97 years to reach a value of $25,000.
Step-by-step explanation:
To find the number of years it will take for Ashley's investment to reach a value of $16,000, we can use the formula for compound interest:
P = P0(1+r)t
where P is the future value, P0 is the present value, r is the growth rate as a decimal, and t is the number of years.
For $16,000:
$16,000 = $9,900(1 + 0.06)t
Divide both sides by $9,900:
1.616 = (1 + 0.06)t
Take the logarithm of both sides to solve for t:
t = log1+0.06(1.616)
Using a scientific calculator, we find that t is approximately 5.07 years.
Similarly, for $25,000:
$25,000 = $9,900(1 + 0.06)t
t = log1+0.06(2.525)
Using a scientific calculator, we find that t is approximately 8.97 years. So, it will take about 5.07 years for Ashley's investment to reach a value of $16,000, and about 8.97 years to reach a value of $25,000.