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.



Answer to a math question 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.

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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}

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}}

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