nicole has the choice of taking out a 30-year loan for $165,000 at 9.1% interest, compounded monthly, or the same loan at 25 years for a higher monthly payment. how much more is the monthly payment for the 25-year loan than the monthly payment for the 30- year loan

Answer:The monthly payment for 25 years is $56.50 more than the monthly payment for 30 years loan.Step-by-step explanation:The formula to be used is :[tex]\frac{p\times r\times (1+r)^{n} }{(1+r)^{n}-1 }[/tex]1st scenario:p = 165000n = [tex]30\times12=360[/tex]r = [tex](\frac{9.1}{12})/100[/tex] = 0.00758Putting the values in the formula we get[tex]\frac{165000\times0.00758 \times (1.00758)^{360} }{(1.00758)^{360}-1 }[/tex]= $1339.0452nd scenario:p = 165000n = [tex]25\times12=300[/tex]r = [tex](\frac{9.1}{12})/100[/tex] = 0.00758Putting the values in the formula we get[tex]\frac{165000\times0.00758 \times (1.00758)^{300} }{(1.00758)^{300}-1 }[/tex]= $1395.540The difference in the monthly payments are = [tex]1395.540-1339.045=56.495[/tex] dollars ≈ $56.50Therefore, the monthly payment for 25 years is $56.50 more than the monthly payment for 30 years loan.