Question

Larry Davis borrows $80,000 at 14 percent interest toward the purchase of a home. His mortgage is for 25 years.

a.How much will his annual payments be? (Although home payments are usually on a monthly basis, we shall do our analysis on an annual basis for ease of computation. We will get a reasonably accurate answer.)

b.How much interest will he pay over the life of the loan?

c.How much should he be willing to pay to get out of a 14 percent mortgage and into a 10 percent mortgage with 25 years remaining on the mortgage?

Assume current interest rates are 10 percent. Carefully consider the timeb value of money. Disregard taxes.

Short answer

a. $11,640

b. $211,000

c. $8,813.40

Step-by-step solution

Part a

Part b

$\begin{array}{c}\mathbf{Total}\mathbf{}\mathbf{Interest}\mathbf{}\mathbf{Payment}\mathbf{=}\mathbf{(}\mathbf{Annual}\mathbf{}\mathbf{payment}\mathbf{\times }\mathbf{Loanlife}\mathbf{)}\mathbf{-}\mathbf{Loan}\mathbf{}\mathbf{Amount}\\ \mathbf{=}\mathbf{(}\mathbf{\$}\mathbf{11}\mathbf{,}\mathbf{640}\mathbf{\times }\mathbf{25}\mathbf{)}\mathbf{-}\mathbf{\$}\mathbf{80}\mathbf{,}\mathbf{000}\\ \mathbf{=}\mathbf{\$}\mathbf{291}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{80}\mathbf{,}\mathbf{000}\\ \mathbf{=}\mathbf{\$}\mathbf{211}\mathbf{,}\mathbf{000}\end{array}$

Part c

$\begin{array}{c}\mathbf{Annual}\mathbf{}\mathbf{payment}\mathbf{=}\frac{\mathbf{Loan}\mathbf{}\mathbf{Value}}{\frac{\left[1-\frac{1}{{(1+r)}^n}\right]}{\mathbf{r}}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{80}\mathbf{,}\mathbf{000}}{\frac{\left[1-\frac{1}{{(1+0.10)}^{25}}\right]}{\mathbf{0}\mathbf{.}\mathbf{10}}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{80}\mathbf{,}\mathbf{000}}{\mathbf{9}\mathbf{.}\mathbf{077}}\\ \mathbf{=}\mathbf{\$}\mathbf{8}\mathbf{,}\mathbf{813}\mathbf{.}\mathbf{50}\end{array}$