Figure 12.69 is a contour diagram of the monthly payment on...

Figure 12.69 is a contour diagram of the monthly payment on a 5 -year car loan as a function of the interest rate and the amount you borrow. The interest rate is $13 \%$ and you borrow $\$ 6000$ for a used car. (a) What is your monthly payment? (b) If interest rates drop to $11 \%$, how much more can you borrow without increasing your monthly payment? (c) Make a table of how much you can borrow without increasing your monthly payment, as a function of the interest rate. (FIGURE CANNOT COPY)

Figure 12.69 is a contour diagram of the monthly payment on a 5 -year car loan as a function of the interest rate and the amount you borrow. The interest rate is $13 \%$ and you borrow $\$ 6000$ for a used car.
(a) What is your monthly payment?
(b) If interest rates drop to $11 \%$, how much more can you borrow without increasing your monthly payment?
(c) Make a table of how much you can borrow without increasing your monthly payment, as a function of the interest rate.
(FIGURE CANNOT COPY)

Key Concepts

Sensitivity Analysis

Sensitivity analysis examines how the variation in output of a model (for example, the monthly loan payment) can be attributed to different variations in its inputs (such as interest rate or borrowed amount). In the context of loans, it helps in understanding the impact of changes in interest rates on the amount one can borrow or the resulting payment amount without altering the overall financial obligation.

Contour Diagrams in Finance

Contour diagrams in finance are graphical representations that show combinations of two variables (such as interest rate and loan amount) that yield the same outcome, like a constant monthly payment amount. They help visualize how changes in one variable can be offset by changes in another while keeping the payment level unchanged.

Loan Amortization

Loan amortization involves calculating the periodic payment required to fully repay a loan over a specified period, taking into account both principal and interest. This concept uses an amortization formula that determines how much of each payment goes toward paying down the principal and how much covers the interest, ensuring the loan is repaid completely by the end of the term.

Interest Rate Conversion

Interest rate conversion is the process of adjusting an annual interest rate to a corresponding periodic rate (such as monthly) when calculating loan payments. This conversion is essential because loan payment formulas typically require the interest rate to be expressed in the same time unit as the payment frequency.

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