Answer: Exponential & $11,709.83
Explanation:
The growth of the investment can be represented by an exponential function because the interest is being compounded quarterly, which means that the interest is being added to the account balance and the account balance is growing exponentially over time.
The formula for the future value of an investment with continuous compounding is:
A = P e^(rt)
Where A is the future value, P is the principal investment, e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate expressed as a decimal, and t is the time in years.
In this case, the principal investment is $10,000, the annual interest rate is 3.2%, and the interest is compounded quarterly, so the quarterly interest rate is 3.2%/4 = 0.8%. The time period is 5 years, so t = 5.
The formula for the future value of an investment with quarterly compounding is: A = P (1 + r/n)^(nt)
Where n is the number of compounding periods per year, which is 4 in this case.
Substituting the values, we get:A = $10,000 (1 + 0.032/4)^(4*5) = $11,709.83
Therefore, the value of the account after 5 years is $11,709.83 rounded to the nearest cent.