Respuesta :
Solution:
To solve this question, we will use the formula below
[tex]\begin{gathered} F.V=P(1+R)^n \\ P=120000 \\ R=\frac{7.5}{100}=0.075 \end{gathered}[/tex]Step 1:
Calculate the interest for 20 years( n=20)
[tex]\begin{gathered} F.v=P(1+R)^n \\ F.v=120,000(1+0.075)^{20} \\ F.v=120,000(1.075)^{20} \\ F.v=\text{ \$}509,742.13 \\ Interest=\text{\$}509,742.13-120,000= \\ Interest=\text{ \$}389,742.13 \end{gathered}[/tex]Step 2:
Calculate the interest for 25 years( n=25)
[tex]\begin{gathered} F,v=P(1+R)^n \\ F,v=120,000(1+0.075)^{25} \\ F.v=120,000(1.075)^{25} \\ F.V=\text{ \$}731800.75 \\ Interest=\text{ \$}731800.75-\text{ \$}120,000 \\ Interest=\text{ \$}611,800.75 \end{gathered}[/tex]The difference in interest will be
[tex]\begin{gathered} 611,800.75-\text{ \$}389,742.13 \\ =\text{ \$}222,058.62 \end{gathered}[/tex]Hence,
The final answer is
The difference in interest is $611,800.75 less $389,742.13 or $222,058.62 in savings by financing for 20 years versus 25 years.
