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.) ...

FINANCIAL ACCOUNTING
10th Edition
ISBN:9781259964947
Author:Libby
Publisher:Libby
Chapter1: Financial Statements And Business Decisions
Section: Chapter Questions
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**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.
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)

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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