The Hogansons purchase a new home for $225,000. They make a 25% down payment and finance the remain a 20-yr mortgage at an annual interest rate of 6.4%, compounded monthly. a) Find the Hogansons' monthly mortgage payment. b) Assume that the Hogansons make every payment for the life of the loan. Find their total payments. c) How much interest do the Hogansons pay? What is the correct formula for this situation? [ ict 1 ¡\ ct 1
The Hogansons purchase a new home for $225,000. They make a 25% down payment and finance the remain a 20-yr mortgage at an annual interest rate of 6.4%, compounded monthly. a) Find the Hogansons' monthly mortgage payment. b) Assume that the Hogansons make every payment for the life of the loan. Find their total payments. c) How much interest do the Hogansons pay? What is the correct formula for this situation? [ ict 1 ¡\ ct 1
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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![**Mortgage Calculation Example**
The Hogansons purchase a new home for $225,000. They make a 25% down payment and finance the remainder with a 20-year mortgage at an annual interest rate of 6.4%, compounded monthly.
### Tasks
a) **Find the Hogansons' monthly mortgage payment.**
b) **Assume that the Hogansons make every payment for the life of the loan. Find their total payments.**
c) **How much interest do the Hogansons pay?**
---
### Formula Selection
**Which is the correct formula for this situation?**
- **Option A**:
\[
P \left( 1 + \frac{i}{c} \right)^{ct} = \left[ \left( 1 + \frac{i}{c} \right)^{ct} - 1 \right] \frac{p}{ \frac{i}{c} }
\]
- **Option B**:
\[
A = \left[ \left( 1 + \frac{i}{c} \right)^{ct} - 1 \right] \frac{p}{ \frac{i}{c} }
\]
### Solution Steps
a) **The Hogansons' monthly mortgage payment is $[ \_\_ ]**.
(Simplify your answer. Do not round until the final answer. Then round to two decimal places as needed. Do not include the $ symbol in your answer.)
b) **The total of the Hogansons' payments is $[ \_\_ ]**.
(Simplify your answer. Do not round until the final answer. Then round to two decimal places as needed. Do not include the $ symbol in your answer.)
c) **The Hogansons pay $[ \_\_ ] in interest.**
(Simplify your answer. Do not round until the final answer. Then round to two decimal places as needed. Do not include the $ symbol in your answer.)
---
### Explanation of the Diagrams
- Both equations provided relate to mortgage calculations.
- In both options, \( P \) represents the principal amount, \( i \) the annual interest rate, \( c \) the compounding periods per year, and \( t \) the total number of years.
- The equation structure involves calculating an annuity payment or future value considering compounding effects.
Please select the appropriate formula and simplify](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe2539764-cbb6-4f84-96a1-bc799fc276f3%2F6430f002-443d-411a-8e9c-e7601ca7f0bd%2Fk03ny04_processed.png&w=3840&q=75)
Transcribed Image Text:**Mortgage Calculation Example**
The Hogansons purchase a new home for $225,000. They make a 25% down payment and finance the remainder with a 20-year mortgage at an annual interest rate of 6.4%, compounded monthly.
### Tasks
a) **Find the Hogansons' monthly mortgage payment.**
b) **Assume that the Hogansons make every payment for the life of the loan. Find their total payments.**
c) **How much interest do the Hogansons pay?**
---
### Formula Selection
**Which is the correct formula for this situation?**
- **Option A**:
\[
P \left( 1 + \frac{i}{c} \right)^{ct} = \left[ \left( 1 + \frac{i}{c} \right)^{ct} - 1 \right] \frac{p}{ \frac{i}{c} }
\]
- **Option B**:
\[
A = \left[ \left( 1 + \frac{i}{c} \right)^{ct} - 1 \right] \frac{p}{ \frac{i}{c} }
\]
### Solution Steps
a) **The Hogansons' monthly mortgage payment is $[ \_\_ ]**.
(Simplify your answer. Do not round until the final answer. Then round to two decimal places as needed. Do not include the $ symbol in your answer.)
b) **The total of the Hogansons' payments is $[ \_\_ ]**.
(Simplify your answer. Do not round until the final answer. Then round to two decimal places as needed. Do not include the $ symbol in your answer.)
c) **The Hogansons pay $[ \_\_ ] in interest.**
(Simplify your answer. Do not round until the final answer. Then round to two decimal places as needed. Do not include the $ symbol in your answer.)
---
### Explanation of the Diagrams
- Both equations provided relate to mortgage calculations.
- In both options, \( P \) represents the principal amount, \( i \) the annual interest rate, \( c \) the compounding periods per year, and \( t \) the total number of years.
- The equation structure involves calculating an annuity payment or future value considering compounding effects.
Please select the appropriate formula and simplify
Expert Solution
Step 1: Define=Monthly payment
Loans are paid by equal fixed monthly payments that carry the payment for interest and loan both.
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