TheMortgageReports.com reported the median price of a home sold in the United States hit a record high in 2020 at just above $\mathrm{\$}320,000$. Juan Carlos Soto, Jr., wants to purchase a new home for $\mathrm{\$}330,500$. Juan puts $20\mathrm{\%}$ down and will finance the remainder of the purchase. Compare the following two mortgage options he has: 15 years at $3.5\mathrm{\%}$ or 20 years at $7.0\mathrm{\%}$. (Use Table 15.1.)

Note: Round your intermediate calculations and final answers to the nearest cent.
a. Calculate Juan's monthly payment for both the 15 and 20 year mortgage?
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b. Calculate Juan's total cost of interest for both the 15 and 20 year mortgage?
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c. What is the difference in interest paid between 15 and 20 year mortgage?
Difference in interest paid
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Step 1 ：$\text{Amount to finance}=330,500\times 0.80=264,400$

Step 2 ：$\text{For the 15 year mortgage at 3.5\%:}$

Step 3 ：$r=\frac{3.5}{12}=0.002917$

Step 4 ：$n=15\times 12=180$

Step 5 ：$P=\frac{0.002917\times 264,400}{1-(1+0.002917{)}^{-180}}=1,889.70$

Step 6 ：$\text{For the 20 year mortgage at 7.0\%:}$

Step 7 ：$r=\frac{7.0}{12}=0.005833$

Step 8 ：$n=20\times 12=240$

Step 9 ：$P=\frac{0.005833\times 264,400}{1-(1+0.005833{)}^{-240}}=2,056.61$

Step 10 ：$\text{For the 15 year mortgage:}$

Step 11 ：$\text{Total payments}=1,889.70\times 180=340,146$

Step 12 ：$\text{Total interest}=340,146-264,400=75,746$

Step 13 ：$\text{For the 20 year mortgage:}$

Step 14 ：$\text{Total payments}=2,056.61\times 240=493,586.40$

Step 15 ：$\text{Total interest}=493,586.40-264,400=229,186.40$

Step 16 ：$\text{Difference in interest paid}=229,186.40-75,746=\boxed{{\displaystyle 153,440.40}}$