Chapter 4, Problem 2P

a.

Summary Introduction

To calculate: Monthly payments.

Explanation of Solution

Formula to calculate monthly payment is as follows:

$\text{Monthly payment}=\text{Principal}\times \left(\text{MLC at 6\% for 25 years}\right)$

$\begin{array}{c}\text{Monthly payment}=\$80,000\times 0.006443\\ =\$515.44\end{array}$

b.

Summary Introduction

To calculate: Interest and principle payments during month 1.

Explanation of Solution

Formula to calculate interest is as follows:

$\text{Interest}=\text{Principle}\times \frac{\text{Interest rate}}{12}$

Substitute equation with $80,000 for principle, 6% for interest rate to calculate interest.

$\begin{array}{c}\text{Interest}=\$80,000\times \frac{6\%}{12}\\ =\$400\end{array}$

Calculation of monthly payment during month 1 is as follows:

$\text{Monthly payment}=\text{Monthly payment}-\text{Interest}$

Substituting equation with 515.44 for monthly payment and $400 for interest to calculate payment during month 1.

$\begin{array}{c}\text{Monthly payment}=\$515.44-\$400\\ =\$115.44\end{array}$

c.

Summary Introduction

To calculate: Total principle and total interest paid over 25 years.

Explanation of Solution

Formula to calculate total payment is as follows:

$\text{Total payment}=\text{Monthly payment}\times 25\times 24$

Substituting equation with $515.44 for monthly payment to calculate total payments.

$\begin{array}{c}\text{Total payment}=\$515.44\times 25\times 24\\ =\$154,632\end{array}$

Total payment is $154,632.

Formula to calculate total interest payment is as follows:

$\text{Total interest payment}=\text{Total payments}-\text{principle payment}$

Substituting equation with $154,632 for total payments and $80,000 for principle payments to calculate total interest payment.

$\begin{array}{c}\text{Total interest payment}=\$154,632-\$80,000\\ =\$74,632\end{array}$

d.

Summary Introduction

To determine: Outstanding loan balance if the loan is repaid at the end of year 10.

Explanation of Solution

Formula to calculate future value is as follows:

$\text{Future value}=\text{Present value}{\left(1+\text{i}\right)}^{\text{n}}$

Substituting equation with $80,000 for present value, 0.50 for I and 120 for n to calculate future value.

$\begin{array}{c}\text{Future value}=\text{\$80,000}{\left(1+0.50\right)}^{120}\\ =\$61,081\end{array}$

e.

Summary Introduction

To calculate: Total monthly interest and principle payments through 10 years.

Explanation of Solution

Formula to calculate total interest payment is as follows:

$\text{Total payments}=\text{Monthly payment}\times \text{n}$

Substituting equation with $515.44 for monthly interest and 120 for n to calculate total payment.

$\begin{array}{c}\text{Total payments}=\$515.44\times 120\\ =\$61,852.80\end{array}$

Formula to calculate total principle payment is as follows:

$\text{Total principle payments}=\text{Loan amount}-\text{Present value of the loan at the end of 10 years}$

Substituting equation with $80,000 for loan amount and $61,081.77 for present value to calculate total principle payment.

$\begin{array}{c}\text{Total principle payments}=\$80,000-\$61,081.77\\ =\$18,918.23\end{array}$

Formula to calculate total interest payment is as follows:

$\text{Total interest payments}=\text{Total payments}-\text{total principle payment}$

Substituting equation with $61,852 for total payments and $18,918.23 for total principle payment to calculate total interest payment.

$\begin{array}{c}\text{Total interest payments}=\$61,852.80-\$18,918.23\\ =\$42,934.57\end{array}$

f.

Summary Introduction

To calculate: Breakdown of interest and principle during month 50.

Explanation of Solution

Present value of the outstanding loan at the end of month 49 is $73,608.28, formula to calculate interest payment is as follows:

$\text{Total interest payments}=\text{outstanding loan balance}\times \text{interest rate}$

Substituting equation with $73,608.28 for outstanding loan and 0.50% for the interest rate.

$\begin{array}{c}\text{Total interest payments}=\$73,608.28\times 0.50\%\\ =\$368.04\end{array}$

Formula to calculate principle payment is as follows:

$\text{Principle payment}=\text{Total payment}-\text{Interest payment}$

Substituting equation with $515.44 for total payment and $368.04 for interest payment to calculate principle payment.

$\begin{array}{c}\text{Principle payment}=\$515.44-\$368.04\\ =\$147.40\end{array}$