Find the payment necessary to amortize a 4% loan of $1800 compounded quarterly, with 19 quarterly payments. The payment size is $ (Round to the nearest cent.)
Find the payment necessary to amortize a 4% loan of $1800 compounded quarterly, with 19 quarterly payments. The payment size is $ (Round to the nearest cent.)
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%
![**Loan Amortization Calculation**
To determine the payment necessary to amortize a 4% loan of $1800 compounded quarterly over 19 quarterly payments, follow this calculation process.
**Formula:**
The formula to determine the periodic payment \( P \) for an amortizing loan is:
\[
P = \frac{r \times PV}{1 - (1 + r)^{-n}}
\]
Where:
- \( PV \) = Present Value (the initial loan amount, $1800)
- \( r \) = Periodic interest rate (annual interest rate divided by the number of compounding periods per year)
- \( n \) = Total number of payments
**Given:**
- Annual Interest Rate = 4%
- Compounded Quarterly = 4 times a year
- Total Payments = 19
**Steps:**
1. Convert the annual interest rate to a quarterly interest rate:
\[
r = \frac{4\%}{4} = 1\%
\]
Convert to decimal:
\[
r = 0.01
\]
2. Substituting these values into the formula to find \( P \):
\[
P = \frac{0.01 \times 1800}{1 - (1 + 0.01)^{-19}}
\]
3. Simplify and calculate \( P \).
**Output:**
You will find that the payment size is approximately \$[calculation result] (rounded to the nearest cent).
**Note:** Complete the calculation to find the final rounded payment size.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb76a34ef-22d3-4cb0-8af6-813d524e1e4e%2F4c74ab4d-8489-464c-8d25-bf8d3e5eb7f6%2F5xd9zfh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Loan Amortization Calculation**
To determine the payment necessary to amortize a 4% loan of $1800 compounded quarterly over 19 quarterly payments, follow this calculation process.
**Formula:**
The formula to determine the periodic payment \( P \) for an amortizing loan is:
\[
P = \frac{r \times PV}{1 - (1 + r)^{-n}}
\]
Where:
- \( PV \) = Present Value (the initial loan amount, $1800)
- \( r \) = Periodic interest rate (annual interest rate divided by the number of compounding periods per year)
- \( n \) = Total number of payments
**Given:**
- Annual Interest Rate = 4%
- Compounded Quarterly = 4 times a year
- Total Payments = 19
**Steps:**
1. Convert the annual interest rate to a quarterly interest rate:
\[
r = \frac{4\%}{4} = 1\%
\]
Convert to decimal:
\[
r = 0.01
\]
2. Substituting these values into the formula to find \( P \):
\[
P = \frac{0.01 \times 1800}{1 - (1 + 0.01)^{-19}}
\]
3. Simplify and calculate \( P \).
**Output:**
You will find that the payment size is approximately \$[calculation result] (rounded to the nearest cent).
**Note:** Complete the calculation to find the final rounded payment size.
Expert Solution
Step 1
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,
