megan borrowed $50,000 at 5% simple interest for 6 years. joseph borrowed $60,000 at 4% simple interest for…

megan borrowed $50,000 at 5% simple interest for 6 years. joseph borrowed $60,000 at 4% simple interest for 8 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 rate expressed as a decimal, and $t$ is the amount of time for the loan, in years. who will have a greater monthly payment, and by how much?\n\nmegan will pay approximately $8 dollars more per month.\nmegan will pay approximately $78 dollars more per month\njoseph will pay approximately $8 dollars more per month.\njoseph will pay approximately $78 dollars more per month.

megan borrowed $50,000 at 5% simple interest for 6 years. joseph borrowed $60,000 at 4% simple interest for 8 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 rate expressed as a decimal, and $t$ is the amount of time for the loan, in years. who will have a greater monthly payment, and by how much?\n\nmegan will pay approximately $8 dollars more per month.\nmegan will pay approximately $78 dollars more per month\njoseph will pay approximately $8 dollars more per month.\njoseph will pay approximately $78 dollars more per month.

Answer

Explanation:

Step1: Calculate Megan's monthly payment

First, convert Megan's rate to decimal: $r_1 = 0.05$, $P_1=50000$, $t_1 = 6$. Substitute into formula $m_1=\frac{P_1 + P_1r_1t_1}{12t_1}$. $m_1=\frac{50000+50000\times0.05\times6}{12\times6}=\frac{50000 + 15000}{72}=\frac{65000}{72}\approx902.78$

Step2: Calculate Joseph's monthly payment

Convert Joseph's rate to decimal: $r_2 = 0.04$, $P_2 = 60000$, $t_2=8$. Substitute into formula $m_2=\frac{P_2+P_2r_2t_2}{12t_2}$. $m_2=\frac{60000+60000\times0.04\times8}{12\times8}=\frac{60000+19200}{96}=\frac{79200}{96}=825$

Step3: Find the difference

Calculate $m_1 - m_2$. $902.78-825 = 77.78\approx78$

Answer:

Megan will pay approximately $78$ dollars more per month.