Question

How much can be saved in totalinterest by financing $120,000 at7.50% for 20 years rather than25 years?

Answer 1

To solve this question, we will use the formula below

`\begin{gathered} F.V=P(1+R)^n \\ P=120000 \\ R=(7.5)/(100)=0.075 \end{gathered}`

Step 1:

Calculate the interest for 20 years( n=20)

`\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}`

Step 2:

Calculate the interest for 25 years( n=25)

`\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}`

The difference in interest will be

`\begin{gathered} 611,800.75-\text{ \$}389,742.13 \\ =\text{ \$}222,058.62 \end{gathered}`

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.