Chapter 7, Problem 1PA

Summary Introduction

To determine:

The reason to choose the loan and calculate the amount of the payment on the home equity and union credit loan.

Introduction:

Interest is the amount which is paid on the principal amount by the borrower to the lender. The rate of interest is fixed on the principal amount at the time of borrowing by the lender.

Answer to Problem 1PA

Solution:

• The rate of interest on union credit is 12% while home credit rate of interest is 8.75 which are lower than the union credit.
• As the home credit is less than the union credit so R should choose the home credit lone because he has to pay less interest on the loan.
• If the he choose the home credit loan then he will have to pay less tax on the interest due to the low rate of interest.
• Since, the home equity is smaller than the union credit that is why home equity loan will be chosen.

Explanation of Solution

given,

Union credit interest rate is 12%.

Home equity interest rate is 8.75%.

Amount of loan is $2,500.

Number of year is 2.

Number of month of payment is 12.

Formula to calculate the union credit payment monthly,

$PMT=PV\times \left(\frac{\frac{i}{m}}{1-{\left(1+\frac{i}{m}\right)}^{-n\times m}}\right)$

Where,

• PMT is Amount of monthly payment.
• PV is amount of loan.
• i is the rate of interest.
• n is the number of years.
• m is the number of payment in a year.

Substitute $2,500 for PV, 12% for I, 12 for m in the above equation and 2 for the n,

$\begin{array}{c}\text{PMT}=\$2,500\times \left(\frac{\frac{0.12}{12}}{1-{\left(1+\frac{0.12}{12}\right)}^{-2\times 12}}\right)\\ =\$2,500\times \left(\frac{0.01}{1-0.79}\right)\\ =\$2,500\times 0.0470\\ =\$117.5\end{array}$

Formula to calculate the home equity payment monthly,

$PMT=PV\times \left(\frac{\frac{i}{m}}{1-{\left(1+\frac{i}{m}\right)}^{-n\times m}}\right)$

Where,

• PMT is Amount of monthly payment.
• PV is amount of loan.
• i is the rate of interest.
• n is the number of years.
• m is the number of payment in a year.

Substitute $2,500 for PV, 8.75% for I, 12 for m in the above equation and 2 for the n,

$\begin{array}{c}\text{PMT}=\$2,500\times \left(\frac{\frac{0.0875}{12}}{1-{\left(1+\frac{0.0875}{12}\right)}^{-2\times 12}}\right)\\ =\$2,500\times \left(\frac{0.0072}{1-0.84}\right)\\ =\$2,500\times 0.045\\ =\$112.5\end{array}$

Hence, home equity is $112.5 and union credit loan is $117.5.