Chapter 7, Problem 1PA

Summary Introduction

To determine:

Monthly payment and total repayment for the bank loan and store financing and reason for lower monthly payment and total repayment of bank loan.

Introduction:

Loan is the amount or thing is taken from another person with the promise of future payment.

Explanation of Solution

Bank loan:

Monthly payment:

Given,

PV is $1,500.

i is 14%.

n is 1 years.

m is 12.

The formula to calculate the amount of monthly payment is,

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

Where,

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

Substitute $1,500 for PV, 14% for i, 1 for n and12 for m in the above equation.

$\begin{array}{c}PMT=\$1,500\times \left(\frac{\frac{0.14}{12}}{1-{\left(1+\frac{0.14}{12}\right)}^{-1\times 12}}\right)\\ =\$1,500\times \frac{0.0116}{1-0.8700}\\ =\$125.70\end{array}$

The monthly payment is $125.70.

Total repayment:

Given,

Monthly repayment is $125.70.

Number monthly payment is 12.

Formula to calculate total repayment is,

$\text{Total repayment}=\text{Monthly payment}\times \text{Number of monthly payment}$

Substitute $125.70 for monthly payment and 12 for number of monthly payment in the above formula.

$\begin{array}{c}\text{Total repayment}=\text{\$125}\text{.70}\times \text{12}\\ =\text{\$1,508}\text{.4}\end{array}$

Total repayment is $1508.4.

Store financing:

Total repayment:

Given,

Loan amount is $1,500.

Simple interest is $180.

Formula to calculate total repayment is,

$\text{Total repayment}=\text{Loan amount}+\text{Simple interest}$

Substitute $1,500 for loan amount and $180 for simple interest in the above formula.

$\begin{array}{c}\text{Total repayment}=\text{\$1,500}+\text{\$180}\\ =\$\text{1,680}\end{array}$

Total repayment is $1,680.

Monthly installment:

Given,

Total repayment is $1,680.

Number of monthly payment is 12.

Formula to calculate monthly payment is,

$\text{Monthlypayment}=\frac{\text{Total repayment}}{\text{Number of monthly payment}}$

Substitute $1,680 for total repayment and 12 for number of monthly payment in the above formula.

$\begin{array}{c}\text{Monthlypayment}=\frac{\$1,680}{\text{12}}\\ =140\end{array}$

Monthly payment is $140.

Working note:

Calculation for simple interest,

$\begin{array}{c}\text{Simple interest}=\text{Rate}\times \text{Loan amount}\\ \text{=}\frac{12}{100}\times \$1,500\\ =\$180\end{array}$

Monthly payment and total repayment is low for bank loan than store financing even when the rate on bank loan is high because interest on bank loan is decreasing with each payment but interest on store loan is on whole loan amount for whole year.

Conclusion

Hence, monthly payment and total repayment is lower for bank loan.