Learn Before
Solving a Loan Interest Application Using a System of Equations
We can also find the principal amounts of different loans given the total interest by translating the problem into a system of equations. For instance, if the total principal owed on a bank loan and a federal loan is $ , and the bank loan has a interest rate while the federal loan has a rate, with a total paid interest of $ , the system is:
- The Principal equation: .
- The Interest equation: . Solving this system using substitution provides the principal for each loan.
0
1
Tags
OpenStax
Intermediate Algebra @ OpenStax
Ch.4 Systems of Linear Equations - Intermediate Algebra @ OpenStax
Algebra
Related
A small business owner is calculating the cost of a short-term loan using the simple interest formula I = Prt. Match each variable from the formula to its correct definition in this financial context.
When a business uses the simple interest formula I = Prt to calculate earnings on a short-term deposit, the interest is calculated only on the original principal and does not compound.
When a business owner uses the simple interest formula I = Prt to calculate the interest on a short-term loan, how must the annual interest rate (r) be expressed to ensure the calculation is correct?
A corporate accountant is using the simple interest formula to calculate the interest earned on a company investment. In this formula, the variable t represents the time the money is invested and must be expressed in units of ________.
A corporate finance intern is calculating the interest on a short-term bridge loan. Arrange the following steps in the correct order to apply the simple interest formula effectively.
Defining the Simple Interest Formula
Standardizing Simple Interest Calculations
Financing Equipment for Logistics Operations
A financial analyst is using the simple interest formula to determine a missing value in a corporate loan report. According to the formula's requirements, how many of the four total variables () must be identified from the loan terms to solve for the remaining unknown value?
A department head is calculating the cost of a short-term equipment lease using the simple interest formula . What does the calculated value of I represent in this professional context?
Simple Interest
Solving for Simple Interest Earned on Areli's Investment
Solving an Investment Interest Application Using a System of Equations
Solving a Loan Interest Application Using a System of Equations
Learn After
A technician is starting a new repair shop and takes out two loans to purchase necessary equipment. The first loan has an interest rate of 5%, and the second loan has an interest rate of 8%. The total amount borrowed is 15,000 dollars, and the total annual interest paid is 900 dollars. Let represent the principal amount of the 5% loan and represent the principal amount of the 8% loan. Match each mathematical component to its correct financial description in the system of equations.
A bakery owner takes out two loans totaling $15,000 to purchase new commercial ovens. The first loan has an annual interest rate of , and the second loan has an annual interest rate of . If the total interest paid after one year is $900, which equation correctly represents the total interest paid on these two loans? (Let be the principal of the loan and be the principal of the loan).
Financing Business Equipment
A logistics coordinator is analyzing two different equipment loans using a system of equations to determine the amount borrowed for each. While the sum of the two loan amounts is used to create the principal equation, the annual interest rates (such as and ) must be used as coefficients in the ____ equation.
A small business owner is using a system of equations to determine the original principal amounts of two separate loans used to buy office equipment.
True or False: To build the interest equation for this system, the owner should multiply the total combined principal by the sum of the two interest rates.