peter wants to borrow $3,000. he has two payment plans to choose from. plan a charges 4% interest over 6…

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?\nplan a has a monthly payment of about $23 less and a total interest charge of $120 less than plan b.\nplan a has a monthly payment of about $23 less and a total interest charge of $120 more than plan b.\nplan a has a monthly payment of about $23 more and a total interest charge of $120 more than plan b.\nplan a has a monthly payment of about $23 more and a total interest charge of $120 less than plan b.

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?\nplan a has a monthly payment of about $23 less and a total interest charge of $120 less than plan b.\nplan a has a monthly payment of about $23 less and a total interest charge of $120 more than plan b.\nplan a has a monthly payment of about $23 more and a total interest charge of $120 more than plan b.\nplan a has a monthly payment of about $23 more and a total interest charge of $120 less than plan b.

Answer

Explanation:

Step1: Calculate total amount for Plan A

For Plan A, $P = 3000$, $r=0.04$, $t = 6$. First find the total amount $A=P+Prt=3000+3000\times0.04\times6=3000 + 720=3720$. Then the monthly payment $m_A=\frac{3720}{12\times6}=\frac{3720}{72}\approx51.67$.

Step2: Calculate total amount for Plan B

For Plan B, $P = 3000$, $r = 0.05$, $t=4$. First find the total amount $A=P+Prt=3000+3000\times0.05\times4=3000+600 = 3600$. Then the monthly payment $m_B=\frac{3600}{12\times4}=\frac{3600}{48}=75$.

Step3: Compare monthly - payments

The difference in monthly payments is $m_B - m_A=75 - 51.67\approx23$.

Step4: Compare total interest charges

The total interest for Plan A is $I_A=3000\times0.04\times6 = 720$. The total interest for Plan B is $I_B=3000\times0.05\times4=600$. The difference in total interest is $I_A - I_B=720 - 600 = 120$. Plan A has a total interest charge of $120$ more than Plan B and a monthly payment of about $23$ less than Plan B.

Answer:

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