120 0.035 1 + 12 -1 (190000 269485.527 - 143.4325x If 1 find the monthly payment that will pay off a loan of $190,000 in 10 years at the interest rate of 3.5%.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![The problem involves finding the monthly payment for a loan using a matrix equation. The matrix equation is given as follows:
\[
\begin{bmatrix}
\left(1 + \frac{0.035}{12}\right) & -1 \\
0 & 1
\end{bmatrix}^{120}
\begin{bmatrix}
190000 \\
x
\end{bmatrix}
=
\begin{bmatrix}
269485.527 - 143.4325x \\
x
\end{bmatrix}
\]
The task is to find the monthly payment that will pay off a loan of $190,000 in 10 years at an interest rate of 3.5%.
**Explanation:**
- The matrix on the left includes calculations for the monthly interest rate \(\frac{0.035}{12}\).
- The matrix exponentiation, denoted by \(^{120}\), refers to the 120 monthly payments over 10 years.
- The vector \(\begin{bmatrix} 190000 \\ x \end{bmatrix}\) represents the loan amount of $190,000 and the unknown monthly payment \(x\).
- The resulting vector \(\begin{bmatrix} 269485.527 - 143.4325x \\ x \end{bmatrix}\) represents the remaining balance and monthly payments after the loan term.
The problem asks you to solve for \(x\), the monthly payment amount.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd93a67bc-9633-4b56-adf6-c32254ee61f9%2F8b60422a-0799-4c9b-a89a-a751783fbf81%2Foabfld9_processed.png&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
