Determine the outstanding principal of the given mortgage. (Assume monthly interest payments and compounding periods.) HINT [See Example 7.] a $100,000, 25-year, 4.3% mortgage after 10 years
Determine the outstanding principal of the given mortgage. (Assume monthly interest payments and compounding periods.) HINT [See Example 7.] a $100,000, 25-year, 4.3% mortgage after 10 years
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%
![Determine the outstanding principal of the given mortgage. (Assume monthly interest payments and compounding periods.) HINT [See Example 7.]
a $100,000, 25-year, 4.3% mortgage after 10 years
Step 1
Note that this question asks us to find the outstanding principal, after the first 10 years, on a 25-year, $100,000 mortgage.
The present value formula can be used to calculate the outstanding principal on a mortgage, but to use this formula, the monthly payment on the mortgage must be known.
¡
P√ [₁=(₁^²+0²"]
¸1 − (1 + i)¯n¸
To calculate the monthly payment PMT on a mortgage valued at PV dollars for n periods at an int est rate of i per period, use the formula PMT = PV|
The given mortgage is $100,000, so PV = 100000
100,000
The 4.3% annual interest rate as a decimal is 0.043, so the monthly interest rate is i =
12
0.043
12
If the investment is for 25 years with monthly payments, then the number of pay periods is n = 25. 12 = 300
300](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcde950f0-76bf-49b0-beb1-b0472364554b%2Faf88a969-e83b-4eed-a36d-cbeae331777a%2Flxbrnrs_processed.png&w=3840&q=75)
Transcribed Image Text:Determine the outstanding principal of the given mortgage. (Assume monthly interest payments and compounding periods.) HINT [See Example 7.]
a $100,000, 25-year, 4.3% mortgage after 10 years
Step 1
Note that this question asks us to find the outstanding principal, after the first 10 years, on a 25-year, $100,000 mortgage.
The present value formula can be used to calculate the outstanding principal on a mortgage, but to use this formula, the monthly payment on the mortgage must be known.
¡
P√ [₁=(₁^²+0²"]
¸1 − (1 + i)¯n¸
To calculate the monthly payment PMT on a mortgage valued at PV dollars for n periods at an int est rate of i per period, use the formula PMT = PV|
The given mortgage is $100,000, so PV = 100000
100,000
The 4.3% annual interest rate as a decimal is 0.043, so the monthly interest rate is i =
12
0.043
12
If the investment is for 25 years with monthly payments, then the number of pay periods is n = 25. 12 = 300
300
Transcribed Image Text:With PV = 100,000, i =
nearest cent.
PMT = PV
PMT =
1
100000
= 1048
0.043
12
i
-n
(1 + i)¬^
1
I
and n =
300, we are now ready to find the monthly payment PMT, by substituting these known values into the formula. Simplify and round the result to the
0.043
12
1 +
0.043
12
-300
X
Thus, the monthly payment on a 25-year, $100,000 mortgage at 4.3% per year is $ 1048
X
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
