3.4 Word ProblemsExample 1: If $8,000 is invested at 6 percent simple annual interest, how much interest is earned
after 3 months?Solution: Since the annual interest rate is 6%, the interest for 1 year isThe interest earned in 3 months is( 0. 06 )($8, 00 0) = $480.—^3 ($480) = $120.
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Example 2: If $10,000 is invested at 10 percent annual interest, compounded semiannually, what is the
balance after 1 year?Solution: The balance after the first 6 months would be10,000 + (10, 000)(0.05) = $10,500.
The balance after one year would be 10,500 + (10, 500)(0.05) = $11,025.Note that the interest rate for each 6-month period is 5%, which is half of the 10% annual rate. The
balance after one year can also be expressed as10,000( 1 气） 2 dollars
- Discount
If a price is小scounted by n percent, then the price becomes (100 - n) percent of the original price.Example 1: A certain customer paid $24 for a dress. If that price represented a 25 percent discount on
the original price of the dress, what was the original price of出e dress?Solution: If pis the original price of the dress, then 0.75p is the discounted price and 0.75p = $24, or p =
$32. The original price of the dress was $32.Example 2: The price of an item is discounted by 20 percent and then this reduced price is discounted
by an additional 30 percent. These two discounts are equal to an overall discount of what percent?Solution: If pis the original price of the item, then 0.8p is the price after the first discount. The price
after the second discount is (0.7)(0.8) p = 0.56p. This represents an overall discount of 44 percent
(100%-56%).- Profit
Gross profit is equal to revenues minus expenses, or selling price minus cost.Example: A certain appliance costs a merchant $30. At what price should the merchant sell the
appliance in order to make a gross profit of 50 percent of the cost of the appliance?Solution: Ifs is the selling price of the appliance, thens -30 = (0.5)(30), ors= $45. The merchant
should sell the appliance for $45.