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Chapter 4: Problem 8

The policy of the Broadway Pawnshop is to lend up to 35\(\%\) of the value of a borrower's collateral. John wants to use a \(\$ 3,000\) ring and a \(\$ 1,200\) necklace as collateral for a loan. What is the maximum amount that he could borrow from Broadway?

Short Answer

Expert verified
The maximum amount John could borrow from Broadway is \$1,470.

Step by step solution

01

Determine the Total Value of Collateral

John has a ring worth \(\$ 3,000\) and a necklace worth \(\$ 1,200\). So, we add those values to get the total value of collateral. That is, \(\$ 3,000 + \$ 1,200 = \$ 4,200\)
02

Calculate the Maximum Loanable Amount

Broadway will lend up to 35% of the value of the collateral. To get this value, multiply the total collateral value by 0.35 (which is the decimal equivalent of 35%). So, \(\$ 4,200 * 0.35 = \$1,470\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Collateral Value
Collateral value is the worth of an asset that a borrower pledges against a loan. It gives lenders a sense of security, knowing there is something of value backing the borrowed funds. In John's case, his collateral consists of a ring worth $3,000 and a necklace worth $1,200. The total collateral value is calculated by simply adding the two individual values: $3,000 for the ring and $1,200 for the necklace, equating to a total of $4,200. Understanding the total collateral value is crucial, as it forms the basis upon which the loan amount is determined.
Loan Calculation
Loan calculation involves determining the amount of money a borrower is eligible to receive based on their collateral鈥檚 value. For Broadway Pawnshop, the calculation is simplified: they will lend up to 35% of the total collateral value. We calculate this by multiplying the total collateral, $4,200, by 0.35. This multiplication gives us the maximum loan amount John could potentially receive from Broadway Pawnshop, which is $1,470. By understanding loan calculations, borrowers can effectively plan and manage their financial needs.
Percentage of Value
The concept of percentage of value is integral in the context of loans involving collateral. At Broadway Pawnshop, they have a policy to offer loans amounting to 35% of the collateral's full value. This means they assess risk and ensure that the loan value is significantly less than the collateral, thus protecting themselves in the event of non-repayment. Calculating percentages involves converting the percentage into a decimal (i.e., 35% becomes 0.35), then multiplying this by the collateral value鈥攊n this instance, $4,200. The result of $1,470 represents how much of the collateral鈥檚 value Broadway will lend, adhering to their lending criterion.
Pawnshop Policies
Pawnshop policies are rules and procedures that guide lending practices. Each pawnshop has unique policies, impacting how much a borrower can receive based on their collateral. Broadway Pawnshop's policy to lend 35% of the item's value is a risk management strategy. By lending less than the total value, they reduce the risk of loss if the borrower defaults. Additionally, these policies often dictate how collateral is valued and the conditions under which it can be reclaimed or sold. Familiarity with these policies helps borrowers understand their borrowing limits and obligations, allowing for informed financial decisions.

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Most popular questions from this chapter

Use the given yearly payment schedule. a. What is the loan amount? b. What is the length of the loan? c. What is the monthly payment? d. What is the total interest paid? e. Construct a scatterplot using the data points (year, loan balance). f. Write a linear regression equation that approximates the year/loan balance relationship. Round to nearest hundredth. g. Write a quadratic regression equation that approximates the year/loan balance relationship. Round to nearest hundredth. h. Write a cubic regression equation that approximates the year/loan balance relationship. Round to the nearest hundredth. $$\begin{array}{|c|c|c|c|}\hline \text { Year } & {\text { Principal Paid }} & {\text { Interest Paid }} & {\text { Loan Balance }} \\ \hline 0 & {} & {} &{\$ 10,000.00} \\ \hline 1 & {\$ 680.52} & {\( 775.41} &{\$ 9,319.48} \\\ \hline 2 & {\) 737.01} & {\( 718.92} &{\$ 8,582.47} \\ \hline 3 & {\) 798.18} & {\( 657.75} &{\$ 7,784.29} \\ \hline 4 & {\) 864.43} & {\( 591.50} &{\$ 6,919.86} \\ \hline 5 & {\) 936.17} & {\( 519.76} &{\$ 5,983.69} \\ \hline 6 & {\) 1,013.88} & {\$ 442.05} &{\$ 4,969.81} \\ \hline 7 & {\( 1,098.03} & {\$ 357.90} &{\$ 3,871.78} \\ \hline 8 & {\) 1,189.16} & {\$ 266.77} &{\$ 2,682.62} \\ \hline 9 & {\( 1,287.86} & {\$ 168.07} &{\$ 1,394.76} \\ \hline 10 & {\) 1,394.76} & {\$ 61.18} &{\$ 0.00} \\ \hline\end{array}$$

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