Describing derivatives in practical terms

In summary, the conversation discusses the units and sign of C'(r), which represents the derivative of the total cost function for a car loan with annual interest rate r%. The units of C'(r) are discussed, with the suggestion of dollars per percent interest. The question of what is meant by "What is its sign?" is also raised, with clarification that it refers to whether the derivative is positive, negative, or zero. The units of r are clarified as a percentage.
  • #1
madgab89
22
0

Homework Statement



Suppose C(r) is the total cost of paying off a car loan borrowed at an annual interest rate of r%. What are the units of C '(r)? What are the units of C'(r)? What is its sign?

Homework Equations


C'(r)=dC/dr


The Attempt at a Solution



So, I figured:

C'(r) = dC/dr
Which is dollars over interest rate(?)...which seems kinda awkward to me. I'm wondering if there's a better solution for what the units of C'(r) would be. (dollars per percent interest?)

And I'm not sure what is meant by "What is it's sign"?
 
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  • #2
What are the units of r?

"What is it's sign" means is it positive or negative ... or zero.
 
  • #3
r is a %
 
  • #4
Okay. So the units of C/r would be ... ?
 

Related to Describing derivatives in practical terms

1. What is a derivative?

A derivative is a financial instrument that derives its value from an underlying asset, such as a stock, bond, or commodity. It represents a contract between two parties, where one party agrees to buy the underlying asset at a specified price and the other party agrees to sell the asset at a specified price in the future.

2. How are derivatives used in the financial world?

Derivatives are used for various purposes in the financial world, including hedging, speculation, and arbitrage. Hedging involves using derivatives to manage risk by offsetting potential losses in one investment with gains in another. Speculation involves making bets on the future price movements of an underlying asset. Arbitrage involves taking advantage of price discrepancies in different markets to make a profit.

3. What are the different types of derivatives?

There are several types of derivatives, including options, futures, forwards, and swaps. Options give the buyer the right, but not the obligation, to buy or sell an underlying asset at a predetermined price on or before a specific date. Futures are contracts to buy or sell an underlying asset at a predetermined price on a specific date in the future. Forwards are similar to futures, but they are not traded on an exchange and have more flexibility in their terms. Swaps involve the exchange of cash flows between two parties based on the performance of an underlying asset.

4. What are the risks associated with derivatives?

Derivatives can be risky investments due to their complex nature and potential for significant losses. The main risks associated with derivatives include market risk, credit risk, liquidity risk, and operational risk. Market risk refers to the potential losses from changes in the value of the underlying asset. Credit risk is the risk of default by the counterparty. Liquidity risk is the risk of not being able to buy or sell a derivative quickly at a fair price. Operational risk refers to potential losses from errors or failures in the trading process.

5. How are derivatives regulated?

Derivatives are regulated by various government agencies and financial institutions to ensure transparency and stability in the financial markets. In the United States, the Commodity Futures Trading Commission (CFTC) and the Securities and Exchange Commission (SEC) are the main regulators of derivatives. The International Swaps and Derivatives Association (ISDA) also plays a role in setting industry standards and promoting best practices for the use of derivatives.

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