Simple Interest
What is the simple interest on $200 for 1 year at a rate of 5%?
Interest = $200×0.05×1 = $10
A store buys a jacket for $30 and wants to sell it with a 50% markup on cost. What is the selling price?
Selling price = 30 + 0.50×30 = $45.
A shirt is on sale for 20% off its $25 original price. What is the sale price?
Sale price = 25 - 0.20×25 = $20.
If you buy a sandwich for $6 and sales tax is 7%, what is the total cost after tax? Round to the nearest cent.
Total = 6 + 0.07×6 = $6.42.
A shirt originally costs $20. It is first marked up 25% and then put on sale for 20% off the new price. What is the final price?
After markup: 20×1.25 = 25.
After 20% off: 25×0.80 = $20.
Final price = $20 (same as original here).
A savings account pays simple interest of 3% per year. If you invest $400, how much interest will you earn in 4 years? What is the total amount after 4 years?
Interest = $400×0.03×4 = $48; Total = $448.
A retailer marks up an item by 40% of cost. If the selling price is $70, what was the cost?
Let cost = c. c + 0.40c = 70 → 1.4c = 70 → c = $50.
An item is marked down 15% from $80. What is the new price? Then find the amount saved.
New price = 80 - 0.15×80 = $68; Savings = $12.
Your restaurant bill is $42.50. If you leave a 15% tip and the sales tax is 8%, calculate the total you pay (tax first, then tip on pre-tax amount).
Tax = 42.50×0.08 = 3.40.
Tip = 42.50×0.15 = 6.375 → 6.38.
Total ≈ 42.50 + 3.40 + 6.38 = $52.28.
An item’s price increases by 15% one year and then decreases by 15% the next year. If the original price is $100, what is the final price? Explain why it is or isn’t $100.
After +15%: 100×1.15 = 115.
After -15%: 115×0.85 = 97.75 ≠ 100.
Write and use a formula to find simple interest. Then find the interest on $1,250 for 2.5 years at 4% simple interest.
Formula: Interest = Principal × Rate × Time. Interest = $1250×0.04×2.5 = $125.
A store increases the price of a pair of shoes by 25% markup on cost. If cost is $48, what is the selling price? Then find the percent increase from the original cost to selling price.
Selling price = 48 + 0.25×48 = $60. Percent increase = 25%.
A store marks an item down 30% and then later marks it down another 10% (both discounts applied to the price after the previous discount). If original price is $200, what is the final price? What is the overall percent decrease from the original?
After first: 200×0.70 = 140. After second: 140×0.90 = 126. Overall decrease = (200-126)/200 = 37%.
An item costs $120 before tax. If the sales tax is 6.25% and you pay with cash, what is the total cost? Also compute the tip you would leave if you add 18% of the pre-tax amount.
Total = 120 + 120×0.0625 = 120 + 7.50 = $127.50.
Tip = 120×0.18 = $21.60.
A population of 5,000 grows by 6% the first year and 4% the second year. What is the population after two years?
Show multiplication steps.
Year1: 5000×1.06 = 5300.
Year2: 5300×1.04 = 5512.
A loan of $900 accrues simple interest at 6% per year. After how many years will the interest be $162?
62 = 900×0.06×t → t = 162 / (900×0.06) = 162/54 = 3 years.
A product has a cost of $80. The store wants a final selling price that gives a 30% profit on selling price (not on cost). What should the selling price be?
(Hint: Let selling price = S; profit = S - cost = 0.30S.)
S - 80 = 0.30S → 0.70S = 80 → S = 80 / 0.7 = $114.29 (approx).
A jacket is on sale for $84 after a 40% markdown. What was the original price?
Let original = p. p×0.60 = 84 → p = 84 / 0.60 = $140.
You purchase three items costing $12.99, $8.50, and $24.75. Sales tax is 7.5%. Find the total tax and the final total. Then find a 20% tip on the pre-tax subtotal.
Subtotal = 12.99+8.50+24.75 = 46.24.
Tax = 46.24×0.075 = 3.468 → 3.47.
Final total ≈ 49.71.
20% tip on pre-tax subtotal = 0.20×46.24 = $9.25.
A store increases a price by 12% and then decreases that new price by 10%. If the original price was $250, what is the final price? What is the net percent change from the original?
After +12%: 250×1.12 = 280.
After -10%: 280×0.90 = 252.
Net change = (252-250)/250 = 0.8% increase.
You invest $2,000 at 3.5% simple interest. After how many years will the total amount be $2,490?
2000 + 2000×0.035×t = 2490 → 2000×0.035×t = 490 → t = 490 / 70 = 7 years.
A wholesaler increases costs twice: first marks up 20% on cost, then later increases that price by another 25% (both markups are on the current price). If original cost is $50, what is the final price? What is the overall percent increase from original cost?
After first: 50×1.20 = 60. After second: 60×1.25 = 75. Overall increase = (75-50)/50 = 50%.
A store advertises "Buy 1 at regular price, get the 2nd at 60% off." If the regular price is $45, what is the total cost for two items? What is the average percent discount per item compared to buying two at full price?
Total = 45 + 45×0.40 = 45 + 18 = $63. Average per item = 63/2 = $31.50. Full price for two = 90; average discount per item = (45-31.5)/45 = 30% per item on average.
A city increases sales tax by 1.25 percentage points, changing it from 6.5% to 7.75%. If a family’s pre-tax monthly purchases average $820, how much more tax will they pay each month because of the increase?
Extra tax = 820×(0.0775 - 0.065) = 820×0.0125 = $10.25 more per month.
A student’s score increases by 20% after extra credit, making the score 84. What was the original score? Then, if that original score had first decreased by 10% and then increased by 20%, what would the final score be? Compare both results and explain.
Let original = x. x×1.20 = 84 → x = 84 / 1.2 = 70. If original first decreased 10%: 70×0.90 = 63, then increased 20%: 63×1.20 = 75. Compare: 84 (after +20%) vs 75 (after -10% then +20%).