Subjects finance mathematics

Interest Problems

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Interest Problems


1. Problem: Find the sales tax rate given the cost of the laptop and the sales tax amount. Step 1: Let the sales tax rate be $r$. Step 2: Sales tax formula: $$\text{Sales Tax} = \text{Cost} \times r$$ Step 3: Substitute values: $$2318.80 = 28985 \times r$$ Step 4: Solve for $r$: $$r = \frac{2318.80}{28985} = 0.08$$ Step 5: Convert to percentage: $$0.08 \times 100\% = 8\%$$ Answer: The sales tax rate is 8%. 2. Problem: Find the amount Kent borrowed given the interest, rate, and time. Step 1: Use the simple interest formula: $$I = P \times r \times t$$ where $I$=interest, $P$=principal, $r$=rate, $t$=time in years. Step 2: Given $I = 45$, $r = 4\% = 0.04$, $t = 0.5$ years. Step 3: Substitute values: $$45 = P \times 0.04 \times 0.5$$ Step 4: Solve for $P$: $$P = \frac{45}{0.04 \times 0.5} = \frac{45}{0.02} = 2250$$ Answer: Kent borrowed 2250. 3. Problem: Find Lea's commission given the total sales and commission rate. Step 1: Commission formula: $$\text{Commission} = \text{Total Sales} \times \text{Rate}$$ Step 2: Given total sales = 37000, rate = 15% = 0.15. Step 3: Calculate commission: $$37000 \times 0.15 = 5550$$ Answer: Lea's commission is 5550. 4. Problem: Calculate total payment Dolly needs to make after borrowing money with interest. Step 1: Use simple interest formula: $$I = P \times r \times t$$ Given $P=3000$, $r=3.5\% = 0.035$, $t=2$ years. Step 2: Calculate interest: $$I = 3000 \times 0.035 \times 2 = 210$$ Step 3: Calculate total payment: $$\text{Total} = P + I = 3000 + 210 = 3210$$ Answer: Dolly will pay 3210 after 2 years. 5. Problem: Calculate the interest Jommel will pay. Step 1: Given $P=1200$, $r=6.5\% = 0.065$, $t=9$ months = 9/12 = 0.75 years. Step 2: Calculate interest: $$I = P \times r \times t = 1200 \times 0.065 \times 0.75 = 58.5$$ Answer: Jommel will pay 58.5 as interest.