Chapter 8, Problem 1PA

Summary Introduction

To determine:

First year cost of car ownership.

Introduction:

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

Explanation of Solution

Given,

Total repayment in one year is $4,281.12.

Property taxes are $300.

Sales taxes are $450.

Title and tags are $40.

Maintenance and usage costs are $1,500.

Insurance is $2,000.

Formula to calculate total first year cost,

Total first year cost = (Total repayment in one year + Property taxes + Sales taxes + Title and tags + Maintenance and usage costs + Insurance)

Substitute $4,281.12 for total repayment in one year, $300 for property taxes, $450 for sales taxes, $40 for title and tags, $1,500 for maintenance and usage cost and $2,000 for insurance in the above formula.

Total first year cost = $4,281.12 + $300 + $450 + $40 + $1,500 + $2,000 = $8,571.12

Total first year cost is $8,571.12.

Working notes:

Calculation for N’s monthly payments,

$\begin{array}{l}PMT=PV\times \left(\frac{\frac{i}{m}}{1-{\left(1+\frac{i}{m}\right)}^{-n\times m}}\right)\\ =\$15,000\times \left(\frac{\frac{0.0665}{12}}{1-{\left(1+\frac{0.0665}{12}\right)}^{-4\times 12}}\right)\\ =\$15,000\times \frac{0.0055}{1-0.7670}\\ =\$356.76\end{array}$

Calculation for total repayment in one year,

Total repayment in one year = (Monthly payment × Number of payment in one year)
= $356.76 × 12
= $4,281.12

Calculation for property taxes,

$\begin{array}{c}\text{Propertey taxes}=\text{Rate}\times \text{Vehicle value}\\ =\frac{2}{100}\times \$15,000\\ =\$300\end{array}$

Calculation for sales taxes,

$\begin{array}{c}\text{Sales taxes}=\text{Rate}\times \text{Sales price}\\ =\frac{3}{100}\times \$15,000\\ =\$450\end{array}$

Conclusion

Hence, total first year cost of car ownership is $8,571.12.