He took out a personal law motorized loan for 23,000 at an interest rate of 7.45% with monthly payments for a term of two years find ones monthly payment rounded to the nearest cent.

To find the monthly payment for the personal loan, we can use the formula for calculating monthly payments on a loan:

M = \dfrac{P \cdot r \cdot (1+r)^n}{(1+r)^n -1}

where:
M = monthly payment,
P = principal amount (loan amount) = $23,000,
r = monthly interest rate = annual interest rate / 12 = 7.45% / 12,
n = total number of payments = 2 years * 12 months/year = 24 payments.

Plugging in the values:

P = 23,000,
r = \dfrac{7.45}{100 \cdot 12},
n = 24.

Now, we can calculate the monthly payment:

M = \dfrac{23,000 \cdot \dfrac{7.45}{100 \cdot 12} \cdot (1+\dfrac{7.45}{100 \cdot 12})^{24}}{(1+\dfrac{7.45}{100 \cdot 12})^{24} -1}

M = \dfrac{23,000 \cdot 0.00620833 \cdot (1+0.00620833)^{24}}{(1+0.00620833)^{24} -1}

M = \dfrac{23,000 \cdot 0.00620833 \cdot 1.20092}{1.20092 -1}

M = \dfrac{180.99}{0.20092}

M = \$900.85

Therefore, the monthly payment rounded to the nearest cent is $900.85.

\boxed{\text{Answer: \$900.85}}