Question

peter wants to borrow $3,000. he has two payment plans to choose from. plan a charges 4% interest over 6 years. plan b charges 5% interest over 4 years. the formula $m = \frac{p + prt}{12t}$ can be used to calculate the monthly payment, $m$, where $p$ is the principle amount borrowed, $r$ is the interest rate expressed as a decimal, and $t$ is the time of the loan, in years. which statement best compares the plans? \
\bigcirc plan a has a monthly payment of about $23 less and a total interest charge of $120 less than plan b. \
\bigcirc plan a has a monthly payment of about $23 less and a total interest charge of $120 more than plan b. \
\bigcirc plan a has a monthly payment of about $23 more and a total interest charge of $120 more than plan b. \
\bigcirc plan a has a monthly payment of about $23 more and a total interest charge of $120 less than plan b.

Explanation:

Step1: Define variables for Plan A

$P = 3000$, $r = 0.04$, $t = 6$

Step2: Calculate Plan A monthly payment

$$ m_A = \frac{3000 + (3000 \times 0.04 \times 6)}{12 \times 6} = \frac{3000 + 720}{72} = \frac{3720}{72} \approx 51.67 $$

Step3: Calculate Plan A total interest

$$ I_A = 3000 \times 0.04 \times 6 = 720 $$

Step4: Define variables for Plan B

$P = 3000$, $r = 0.05$, $t = 4$

Step5: Calculate Plan B monthly payment

$$ m_B = \frac{3000 + (3000 \times 0.05 \times 4)}{12 \times 4} = \frac{3000 + 600}{48} = \frac{3600}{48} = 75 $$

Step6: Calculate Plan B total interest

$$ I_B = 3000 \times 0.05 \times 4 = 600 $$

Step7: Compare monthly payments

$$ m_B - m_A = 75 - 51.67 \approx 23.33 $$

Step8: Compare total interest

$$ I_A - I_B = 720 - 600 = 120 $$

Answer:

Plan A has a monthly payment of about $23 less and a total interest charge of $120 more than plan B.