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?\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?\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

For Megan, $P = 50000$, $r=0.05$, $t = 6$. Substitute into the formula $m=\frac{P + Prt}{12t}$: [ \begin{align*} m_{Megan}&=\frac{50000+50000\times0.05\times6}{12\times6}\ &=\frac{50000 + 15000}{72}\ &=\frac{65000}{72}\ &\approx902.78 \end{align*} ]

Step2: Calculate Joseph's monthly payment

For Joseph, $P = 60000$, $r = 0.04$, $t=8$. Substitute into the formula $m=\frac{P + Prt}{12t}$: [ \begin{align*} m_{Joseph}&=\frac{60000+60000\times0.04\times8}{12\times8}\ &=\frac{60000+19200}{96}\ &=\frac{79200}{96}\ & = 825 \end{align*} ]

Step3: Find the difference

$m_{Megan}-m_{Joseph}=902.78 - 825=77.78\approx78$

Answer:

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