Mathematics, 26.07.2019 08:30 trishinada63
Dusty has the choice of taking out a 25-year loan for $165,000 at 9.1% interest, compounded monthly, or the same loan at 20 years for a higher monthly payment. how much more is the monthly payment for the 20 -year loan than the monthly payment for the 25-year loan?
Answers: 2
![\text{PV of annuity}=P\left[\dfrac{1-(1+r)^{-n}}{r}\right]](/tpl/images/0134/2876/09efe.png)
![\Rightarrow 165000=P\left[\dfrac{1-(1+\frac{0.091}{12})^{-25\times 12}}{\frac{0.091}{12}}\right]](/tpl/images/0134/2876/b1e72.png)
![\Rightarrow P=\dfrac{165000}{\left[\dfrac{1-(1+\frac{0.091}{12})^{-300}}{\frac{0.091}{12}}\right]}=\$1395.99](/tpl/images/0134/2876/710d5.png)
![\Rightarrow 165000=P\left[\dfrac{1-(1+\frac{0.091}{12})^{-20\times 12}}{\frac{0.091}{12}}\right]](/tpl/images/0134/2876/c10c5.png)
![\Rightarrow P=\dfrac{165000}{\left[\dfrac{1-(1+\frac{0.091}{12})^{-240}}{\frac{0.091}{12}}\right]}=\$1495.17](/tpl/images/0134/2876/bc13b.png)
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