Problem 55 - Prealgebra

Question

On a certain home mortgage, there is a monthly payment of \(\$ 9.66\) for every \(\$ 1,000\) that is borrowed. What is the monthly payment on this type of loan if \(\$ 143,000\) is borrowed?

Step-by-Step Solution

Answer

The monthly payment for a $143,000 loan is $1,381.38.

Step 1: Determine the amount for 1,000 units

First, we need to determine how many units of \(1,000 are there in \)143,000. This is found by dividing the total loan amount, \(143,000, by \)1,000. The calculation is: \[ \frac{143,000}{1,000} = 143 \]So, there are 143 units of \(1,000 in \)143,000.

Step 2: Calculate the total monthly payment

Now that we know there are 143 units of \(1,000, and each unit incurs a \)9.66 monthly payment, we can find the total monthly payment by multiplying the number of units by the monthly payment per unit.The calculation is: \[ 143 \times 9.66 = 1381.38 \]Therefore, the total monthly payment for a \(143,000 loan is \)1,381.38.

Key Concepts

Loan Payment Calculation

Understanding how to calculate loan payments is essential for making smart financial decisions. When you borrow money, you typically have to make regular payments to the lender. These payments consist of both the principal (the original amount borrowed) and the interest (the cost of borrowing the money).
For a simple loan, such as in the provided exercise, each $1,000 borrowed incurs a specific monthly cost. In this example, that cost is $9.66 per $1,000 borrowed. To calculate the total monthly payment on any loan:

• First, determine how many $1,000 units are in the total loan amount. Divide the total amount borrowed by 1,000.
• Then, multiply the number of units by the monthly payment per unit.

This method ensures you accurately calculate the monthly payment, which is crucial for your budgeting.

Monthly Mortgage Payment

Mortgages are loans specifically for purchasing property. Calculating the monthly mortgage payment is a bit different from calculating payments on a simpler loan, and it usually involves interest over a long period. However, in our exercise, the mortgage payment is in a simplified form, where interest has already been factored into the monthly payment amount of $9.66 per $1,000 borrowed.
In the real world, most mortgages require not just principal and interest payments, but also take into account insurance and taxes. Yet, understanding the basic arithmetic of multiplying units is a good starting point to grasp more complex calculations. Key aspects of a realistic mortgage payment include:

• Principal payment - reducing the money you borrowed.
• Interest payment - expense for borrowing the principal.
• Taxes and home insurance - which could be included in escrow payments.

Mastering these calculations helps you understand how your monthly payment is determined.

Basic Arithmetic Operations

At the core of calculating loan payments is using basic arithmetic operations. These operations include addition, subtraction, multiplication, and division – the core building blocks of mathematics. In this exercise:

• We used division to find the number of $1,000 units in the total amount borrowed. Specifically, dividing the loan amount of $143,000 by $1,000 resulted in 143 units.
• We then used multiplication to find the total monthly payment by multiplying the number of units (143) by the cost per unit ($9.66), arriving at the total monthly payment of $1,381.38.

By practicing these basic arithmetic operations, you can handle a range of calculations not just in loans, but in all areas of life that involve numbers. Understanding how to apply these operations efficiently empowers you to manage your finances and make informed decisions.