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# A poor, underpaid math teacher gets a credit for 3000e to buy a motorcycle. The credit goes over 2 years, the payments are monthly due, and the nominal interest rate is 2% payable monthly of course. $a$ How much is the monthly annuity?

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## Answer to a math question A poor, underpaid math teacher gets a credit for 3000e to buy a motorcycle. The credit goes over 2 years, the payments are monthly due, and the nominal interest rate is 2% payable monthly of course. $a$ How much is the monthly annuity?

Santino
4.5
To find the monthly annuity payment for the loan, we can use the formula for the monthly payment of a loan:

PMT = \dfrac{P \cdot r \cdot $1+r$^n}{$1+r$^n - 1}

where:

P = 3000 $principal amount of the loan$

r = \dfrac{2\%}{12} = 0.02/12 $monthly interest rate$

n = 2\cdot 12 = 24 $total number of payments$

Plugging in the values into the formula:

PMT = \dfrac{3000 \cdot \left$\dfrac{0.02}{12}\right$ \cdot \left$1 + \dfrac{0.02}{12}\right$^{24}}{\left$1 + \dfrac{0.02}{12}\right$^{24} - 1}

Calculating above expression gives:

PMT \approx \dfrac{3000 \cdot 0.00166667 \cdot 1.02083333^{24}}{1.02083333^{24} - 1} \approx \dfrac{5}{3000}\dfrac{1.90695}{0.00217} \approx $126.41 Therefore, the monthly annuity payment is$\$126.41$.

\boxed{PMT \approx \\$126.41}

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