Find the payment necessary to amortize a 8% loan of $800 compounded quarterly, with 9 quarterly payments. The payment size is $ (Round to the nearest cent.) ...
Find the payment necessary to amortize a 8% loan of $800 compounded quarterly, with 9 quarterly payments. The payment size is $ (Round to the nearest cent.) ...
Chapter1: Financial Statements And Business Decisions
Section: Chapter Questions
Problem 1Q
Related questions
Question
![**Finding the Payment for Loan Amortization**
To determine the necessary payment to amortize an 8% loan of $800 compounded quarterly, with 9 quarterly payments, follow these steps.
### Problem Statement
- **Loan Amount:** $800
- **Interest Rate:** 8% compounded quarterly
- **Total Payments:** 9 quarterly payments
### Required Calculation
Calculate the payment size needed per quarter using the loan amortization formula.
### Formula for Amortization
The formula to calculate the payment for a loan amortized over periodic payments is:
\[ P = \frac{r \cdot PV}{1 - (1 + r)^{-n}} \]
Where:
- \( P \) = Payment amount per period
- \( r \) = Periodic interest rate (annual rate divided by number of compounding periods per year)
- \( PV \) = Present value or loan amount
- \( n \) = Total number of payments
### Calculation Specifics
1. **Convert Annual Interest Rate to Quarterly Rate:**
- \( r = \frac{8\%}{4} = 2\% \)
2. **Plug Values into Formula:**
- \( P = \frac{0.02 \times 800}{1 - (1 + 0.02)^{-9}} \)
3. **Solve for \( P \) and Round to the Nearest Cent.**
### Answer Box
- The payment size is $\[ \ \].
### Note
Please round your final answer to the nearest cent for accuracy.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb76a34ef-22d3-4cb0-8af6-813d524e1e4e%2F6f710fa5-ec46-4fdc-8476-4346f5184524%2Fda0uvk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Finding the Payment for Loan Amortization**
To determine the necessary payment to amortize an 8% loan of $800 compounded quarterly, with 9 quarterly payments, follow these steps.
### Problem Statement
- **Loan Amount:** $800
- **Interest Rate:** 8% compounded quarterly
- **Total Payments:** 9 quarterly payments
### Required Calculation
Calculate the payment size needed per quarter using the loan amortization formula.
### Formula for Amortization
The formula to calculate the payment for a loan amortized over periodic payments is:
\[ P = \frac{r \cdot PV}{1 - (1 + r)^{-n}} \]
Where:
- \( P \) = Payment amount per period
- \( r \) = Periodic interest rate (annual rate divided by number of compounding periods per year)
- \( PV \) = Present value or loan amount
- \( n \) = Total number of payments
### Calculation Specifics
1. **Convert Annual Interest Rate to Quarterly Rate:**
- \( r = \frac{8\%}{4} = 2\% \)
2. **Plug Values into Formula:**
- \( P = \frac{0.02 \times 800}{1 - (1 + 0.02)^{-9}} \)
3. **Solve for \( P \) and Round to the Nearest Cent.**
### Answer Box
- The payment size is $\[ \ \].
### Note
Please round your final answer to the nearest cent for accuracy.
Expert Solution
Step 1
Time value of money :— According to this concept, value of money in present day is greater than the value of same sum of money in future date.
Present value :— It is the value of future cash flows in present day.
Present value = Future Value/(1+i)n
Or
Present value = Periodic cash flow × Present Value Annuity Factor @i% for n Period
Where, i = Periodic interest rate
n = Number of period
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