Final answer:
Heather's account balance will reach $14,989.87 in approximately 12.69 years.
Step-by-step explanation:
To find the length of time it will take for the account balance to reach $14,989.87, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the final account balance, which is $14,989.87
- P is the initial investment, which is $3,377
- r is the annual interest rate, which is 8%
- n is the number of times the interest is compounded per year, which is 2
- t is the time in years
Plugging in these values, we have:
$14,989.87 = $3,377(1 + 0.08/2)^(2t)
Simplifying further:
4.442 = (1.04)^2t
Taking the logarithm of both sides:
log(4.442) = log[(1.04)^2t]
Using logarithmic properties, we can bring down the exponent:
log(4.442) = 2t log(1.04)
Dividing both sides by 2 log(1.04):
t = log(4.442) / (2 log(1.04))
Using a calculator, we find that t ≈ 12.69 years.