Question 1172544: You are the owner of four Taco Bell restaurant locations. You have a business loan with Citizens Bank taken out 60 days ago that is due in 90 days. The amount of the loan is $70,000, and the rate is 9.5% using ordinary interest.
You currently have some excess cash. You have the choice of sending Citizens $25,000 now as a partial payment on your loan or purchasing an additional $25,000 of serving supplies such as food containers, cups, and plastic dinnerware for your inventory at a special discount price that is "10% off" your normal cost of these items.
How much interest (in $) will you save on this loan if you make the partial payment and don't purchase the additional serving supplies? (Round your answer to two decimal places.)
How much (in $) will you save by purchasing the discounted serving supplies and not making the partial payment?
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's break down each scenario to determine the savings.
**Scenario 1: Partial Payment on Loan**
1. **Calculate the total loan term:**
* The loan is due in 90 days.
* It was taken out 60 days ago.
* The remaining loan term is 90 - 60 = 30 days.
2. **Calculate the original interest:**
* Principal (P) = $70,000
* Rate (R) = 9.5% or 0.095
* Time (T) = 90/360 (ordinary interest uses 360 days)
* Interest = P * R * T = 70000 * 0.095 * (90/360) = $1662.50
3. **Calculate the interest after 60 days (before partial payment):**
* Interest = P * R * T = 70000 * 0.095 * (60/360) = $1108.33 (approximately)
4. **Calculate the remaining principal after partial payment:**
* Remaining principal = $70,000 - $25,000 = $45,000
5. **Calculate the interest on the remaining principal for the remaining 30 days:**
* Interest = P * R * T = 45000 * 0.095 * (30/360) = $356.25
6. **Calculate the total interest paid with the partial payment:**
* Total interest = Interest for 60 days + Interest for 30 days = $1108.33 + $356.25 = $1464.58
7. **Calculate the interest saved:**
* Interest saved = Original interest - Total interest with partial payment = $1662.50 - $1464.58 = $197.92
**Scenario 2: Purchasing Discounted Supplies**
1. **Calculate the discount amount:**
* Discount rate = 10% or 0.10
* Discount amount = $25,000 * 0.10 = $2,500
2. **Savings:**
* The savings by purchasing the discounted supplies is the discount amount, $2,500.
**Answers**
* **Interest saved with partial payment:** $197.92
* **Savings from purchasing discounted supplies:** $2,500.00
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