The formula that approximates the annual interest rate r of...

The formula that approximates the annual interest rate $r$ of a monthly installment loan is given by $$r=\frac{\left[\frac{24(N M-P)}{N}\right]}{\left(P+\frac{N M}{12}\right)}$$ where $N$ is the total number of payments, $M$ is the monthly payment, and $P$ is the amount financed. a. Approximate the annual interest rate for a five-year car loan of $\$ 28,000$ that has monthly payments of $\$ 525 .$ b. Simplify the expression for the annual interest rate $r$, and then rework part (a).

The formula that approximates the annual interest rate $r$ of a monthly installment loan is given by
$$r=\frac{\left[\frac{24(N M-P)}{N}\right]}{\left(P+\frac{N M}{12}\right)}$$
where $N$ is the total number of payments, $M$ is the monthly payment, and $P$ is the amount financed.
a. Approximate the annual interest rate for a five-year car loan of $\$ 28,000$ that has monthly payments of $\$ 525 .$
b. Simplify the expression for the annual interest rate $r$, and then rework part (a).

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Algebraic Expression Simplification

Simplifying complex formulas involves reducing expressions into simpler, more manageable forms without changing their fundamental meaning. In financial contexts, such simplifications make it easier to substitute numerical values, analyze the sensitivity of the rate to changes in loan parameters, and derive a clearer understanding of the dependency between variables.

Annual Interest Rate Approximation

The annual interest rate approximation is a method used to estimate the yearly cost of borrowing based on the relationship between the amount financed, the regular payment amount, and the total number of payments. This approximation allows borrowers to compare loans and understand the effective rate they will pay annually, even when interest is compounded or calculated on a monthly basis.

Installment Loan Fundamentals

An installment loan involves borrowing a specific amount that is repaid over a predetermined period through regular, typically monthly, payments. Understanding the principal amount financed, the frequency and total count of payments, and the periodic payment size is essential for determining the cost and structure of the loan.

Transcript

Please give Ace some feedback