We appreciate your visit to Which of these expressions can be used to calculate the monthly payment for a 30 year loan for tex 190 000 tex at tex 11. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To determine the correct expression for calculating the monthly payment for a 30-year loan of [tex]$190,000 at an annual interest rate of 11.4%, compounded monthly, we can use the standard loan amortization formula:
The formula for the monthly payment \( P \) is:
\[
P = \frac{L \cdot c(1 + c)^n}{(1 + c)^n - 1}
\]
Where:
- \( L \) is the loan amount ($[/tex]190,000 in this case).
- [tex]\( c \)[/tex] is the monthly interest rate.
- [tex]\( n \)[/tex] is the total number of payments.
Let's break it down step-by-step:
1. Calculate the Monthly Interest Rate:
- The annual interest rate is 11.4%, or 0.114 as a decimal.
- To find the monthly interest rate, divide the annual rate by 12:
[tex]\[
c = \frac{0.114}{12} = 0.0095
\][/tex]
2. Determine the Number of Payments:
- For a 30-year loan with monthly payments, calculate:
[tex]\[
n = 30 \times 12 = 360
\][/tex]
3. Use the Formula:
- Substitute the values into the formula:
[tex]\[
P = \frac{190,000 \cdot 0.0095(1 + 0.0095)^{360}}{(1 + 0.0095)^{360} - 1}
\][/tex]
4. Identify the Correct Expression:
- Comparing the provided options with the formula above:
- Option A:
[tex]\[
\frac{190,000 \cdot 0.0095(1 + 0.0095)^{360}}{(1 + 0.0095)^{360} - 1}
\][/tex]
- This matches exactly with our derived formula.
Thus, the correct expression used to calculate the monthly payment is Option A.
The formula for the monthly payment \( P \) is:
\[
P = \frac{L \cdot c(1 + c)^n}{(1 + c)^n - 1}
\]
Where:
- \( L \) is the loan amount ($[/tex]190,000 in this case).
- [tex]\( c \)[/tex] is the monthly interest rate.
- [tex]\( n \)[/tex] is the total number of payments.
Let's break it down step-by-step:
1. Calculate the Monthly Interest Rate:
- The annual interest rate is 11.4%, or 0.114 as a decimal.
- To find the monthly interest rate, divide the annual rate by 12:
[tex]\[
c = \frac{0.114}{12} = 0.0095
\][/tex]
2. Determine the Number of Payments:
- For a 30-year loan with monthly payments, calculate:
[tex]\[
n = 30 \times 12 = 360
\][/tex]
3. Use the Formula:
- Substitute the values into the formula:
[tex]\[
P = \frac{190,000 \cdot 0.0095(1 + 0.0095)^{360}}{(1 + 0.0095)^{360} - 1}
\][/tex]
4. Identify the Correct Expression:
- Comparing the provided options with the formula above:
- Option A:
[tex]\[
\frac{190,000 \cdot 0.0095(1 + 0.0095)^{360}}{(1 + 0.0095)^{360} - 1}
\][/tex]
- This matches exactly with our derived formula.
Thus, the correct expression used to calculate the monthly payment is Option A.
Thanks for taking the time to read Which of these expressions can be used to calculate the monthly payment for a 30 year loan for tex 190 000 tex at tex 11. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
