Solve each problem. See Example 4. Cody sells some property for $240,000. The money will be paid off in two ways: a short-term note at 2% interest and a long-term note at 2.5%. Find the amount of each note if the total annual interest paid is $5500.

Verified step by step guidance

1. Let the amount of the short-term note be $x$ and the amount of the long-term note be $y$.
2. Set up the equation for the total amount: $x + y = 240,000$.
3. Set up the equation for the total interest: $0.02x + 0.025y = 5,500$.
4. Solve the first equation for $x$: $x = 240,000 - y$.
5. Substitute $x = 240,000 - y$ into the second equation and solve for $y$.

Key Concepts

Interest Calculation

Interest calculation is the process of determining the amount of money earned or paid on a principal amount over a specific period. In this problem, the interest rates of 2% and 2.5% are applied to the respective notes, and the total interest earned from both notes must equal $5,500 annually. Understanding how to calculate interest using the formula I = P * r, where I is interest, P is principal, and r is the rate, is essential for solving the problem.

System of Equations

A system of equations is a set of two or more equations with the same variables. In this scenario, we can define two variables representing the amounts of the short-term and long-term notes. By setting up equations based on the total amount of $240,000 and the total interest of $5,500, we can solve for the unknowns using methods such as substitution or elimination.

Principal Amounts

The principal amount refers to the initial sum of money that is invested or loaned, from which interest is calculated. In this problem, the total principal amount of $240,000 is divided between the short-term and long-term notes. Understanding how to allocate this total into two parts while considering the different interest rates is crucial for determining the amounts of each note.