Answer:
Explanation:
To calculate the amount Carl will have in the savings account after 6 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case, Carl deposited $3,800 with an annual interest rate of 2.0% (or 0.02 as a decimal). The interest is compounded annually (n = 1) and the duration is 6 years (t = 6).
Plugging in these values into the formula:
A = 3800(1 + 0.02/1)^(1*6)
Simplifying the equation:
A = 3800(1 + 0.02)^6
A = 3800(1.02)^6
Using a calculator or performing the calculations manually:
A ≈ 3800(1.1268250306)
A ≈ 4286.19
Therefore, Carl will have approximately $4,286.19 in the savings account after 6 years. Rounded to the nearest dollar, the answer would be $4,286.