Given an initial investment of A that earns an annual rate R, compounded m times a year for a total of n years, the future value, FV, is computed as:

$FV = A\left(1 + \frac{R}{m}\right)^{m \times n}$

Substituting the values:

• FV = $100,000
• R = 12% = 0.12
• m = 12 (monthly compounding)
• n = 5 years

$`$100`,000 = A\left(1 + \frac{0.12}{12}\right)^{12 \times 5}$$

$`$100`,000 = A(1.01)^{60}$$

A = \frac{100,000}{1.01^{60}} = \frac{100,000}{1.8167} \approx \`$55`,045

The correct answer is B ($55,045).