To find the worth of the investment after 12 years, we can apply the formula for compound interest, which is A = P(1 + r/n)^(nt).
Here,
A is the amount of money accumulated after n years, including interest,
P is the principal amount (the initial amount of money),
r is the annual interest rate (in decimal),
n is the number of times that interest is compounded per year, and
t is the number of years the money is invested for.
Given parameters are:
P (principal) = $3500,
r (annual interest rate in decimal) = 0.0375 (3.75 % interest rate converted to decimal form by dividing by 100),
t (time in years) = 12,
and n (interest is compounded annually) = 1.
Since the interest is compounded annually, it is calculated once per year, therefore, n = 1.
Inserting these values into the formula, we get
A = 3500 * (1 + 0.0375/1)^(1*12).
Evaluating inside of the brackets first, according to the order of operations (also known as BIDMAS/BODMAS/PEDMAS), we have,
A = 3500 * (1 + 0.0375)^(1*12).
This simplifies to
A = 3500 * (1.0375)^(12).
After performing the calculations, we round off the result to the nearest whole number (as we are looking for the dollar amount, it doesn't make sense to have cents in this context).
So, the investment is worth approximately $5444 after 12 years.