Step 1 :Given the following values:
Step 2 :Principal (P) = $3700
Step 3 :Nominal Rate (r) = 4.8% or 0.048 in decimal
Step 4 :Frequency of Conversion (n) = 2 times per year (semi-annually)
Step 5 :Time (t) = 10 years
Step 6 :We can calculate the future value (FV) of the investment using the formula: \(FV = P * (1 + r/n)^{nt}\)
Step 7 :Substituting the given values into the formula, we get: \(FV = 3700 * (1 + 0.048/2)^{2*10}\)
Step 8 :Calculating the future value, we get: \(FV = 5945.670763758267\)
Step 9 :Rounding to the nearest cent, the future value of the investment is $5945.67
Step 10 :Final Answer: The future value of the investment is \(\boxed{5945.67}\)