Final answer:
To determine how many years it will take for the account to grow to at least $8000 with a $5000 deposit and 6% interest, we can use the compound interest formula. After trial and error, the answer is 8 years.
Step-by-step explanation:
To determine how many years it will take for the account to grow to at least $8000, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
- A = the final amount
- P = the initial principal (deposit)
- r = annual interest rate (as a decimal)
- n = number of times the interest is compounded per year
- t = number of years
In this case, P = $5000, r = 6% or 0.06, and A = $8000. We want to find t. Plugging in the values, we get:
$8000 = $5000(1 + 0.06/n)^(nt)
Simplifying further, we have:
(1 + 0.06/n)^(nt) = $8000/$5000 = 1.6
Since the answer options are in whole numbers of years, we can directly calculate the value of nt by trial and error. After trying a few values, we find that when nt = 8, the left side of the equation becomes approximately 1.6. Therefore, the answer is 8 years (Option B).