Slopes R Us needs to borrow $100,000 to increase its inventory of ski equipment for the upcoming season. The owner is confident that she will sell most, if not all, of the new inventory during the winter, so she wishes to borrow the money for only five months. Her bank has offered her a simple interest amortized loan at 8-% interest. (Round your answers to the nearest cent.) (a) Find the size of the monthly bank payment. 24 (b) Prepare an amortization schedule for all five months of the loan. Amount Payment Principal Interest Total Due after Number Portion Portion Payment Payment

Essentials Of Investments
11th Edition
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Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
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Chapter1: Investments: Background And Issues
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### Example of Simple Interest Amortized Loan Calculation

Slopes R Us needs to borrow $100,000 to increase its inventory of ski equipment for the upcoming season. The owner is confident that she will sell most, if not all, of the new inventory during the winter, so she wishes to borrow the money for only five months.

#### Loan Details
1. **Principal Amount**: $100,000
2. **Interest Rate**: \( 8 \frac{7}{8} \% \) per annum (8.875%)
3. **Loan Duration**: 5 months

Her bank has offered her a simple interest amortized loan.

### Tasks

**(a) Find the size of the monthly bank payment.**

To find the monthly payment amount, use the amortization formula for a simple interest loan:
\[ PMT = \frac{P \times r \times (1 + r)^n}{(1 + r)^n - 1} \]
where:
- \( PMT \) = monthly payment
- \( P \) = principal loan amount
- \( r \) = monthly interest rate
- \( n \) = number of payments

Plugging in the numbers:
- \( P = 100,000 \)
- Annual interest rate = 8.875%, so the monthly interest rate \( r = \frac{8.875\%}{12} = 0.73958\% = 0.0073958 \)
- \( n = 5 \)

**(b) Prepare an amortization schedule for all five months of the loan.**

An amortization schedule is a table detailing each periodic payment on an amortizing loan (typically a mortgage), as generated by an amortization calculator. 

### Amortization Schedule Template

| Payment Number | Principal Portion | Interest Portion | Total Payment | Amount Due after Payment |
|----------------|-------------------|------------------|---------------|--------------------------|
|       0        |         -         |         -        |        -      |         $100,000         |
|       1        |         $         |         $        |        $      |             $            |
|       2        |         $         |         $        |        $      |             $            |
|       3        |         $         |         $        |        $      |             $            |
|       4        |         $
Transcribed Image Text:### Example of Simple Interest Amortized Loan Calculation Slopes R Us needs to borrow $100,000 to increase its inventory of ski equipment for the upcoming season. The owner is confident that she will sell most, if not all, of the new inventory during the winter, so she wishes to borrow the money for only five months. #### Loan Details 1. **Principal Amount**: $100,000 2. **Interest Rate**: \( 8 \frac{7}{8} \% \) per annum (8.875%) 3. **Loan Duration**: 5 months Her bank has offered her a simple interest amortized loan. ### Tasks **(a) Find the size of the monthly bank payment.** To find the monthly payment amount, use the amortization formula for a simple interest loan: \[ PMT = \frac{P \times r \times (1 + r)^n}{(1 + r)^n - 1} \] where: - \( PMT \) = monthly payment - \( P \) = principal loan amount - \( r \) = monthly interest rate - \( n \) = number of payments Plugging in the numbers: - \( P = 100,000 \) - Annual interest rate = 8.875%, so the monthly interest rate \( r = \frac{8.875\%}{12} = 0.73958\% = 0.0073958 \) - \( n = 5 \) **(b) Prepare an amortization schedule for all five months of the loan.** An amortization schedule is a table detailing each periodic payment on an amortizing loan (typically a mortgage), as generated by an amortization calculator. ### Amortization Schedule Template | Payment Number | Principal Portion | Interest Portion | Total Payment | Amount Due after Payment | |----------------|-------------------|------------------|---------------|--------------------------| | 0 | - | - | - | $100,000 | | 1 | $ | $ | $ | $ | | 2 | $ | $ | $ | $ | | 3 | $ | $ | $ | $ | | 4 | $
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