MATH 1012 Section 6.6 Solving Application Problems with Percent Bland

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1 MATH 1012 Section 6.6 Solving Application Problems with Percent Bland Office Max sells a flat panel computer monitor for $299. If the sales tax rate is 5%, how much tax is paid? What is the total cost of the flat panel computer monitor? The sales tax would be $ The total cost of the monitor would be the original price plus the sales tax. The total cost of the monitor is $ The sales tax on a $14,800 Honda Civic is $962. Find the rate of the sales tax. Scott Samuels had pharmaceutical sales of $42,500 last month. If his commission rate is 9%, find the amount of his commission.

2 MATH 1012 Section 6.6 Solving Application Problems with Percent Bland Finding the Percent of Increase/decrease Step 1) Use Subtraction to find the amount of increase/decrease. Step 2) Use the percent proportion to find the percent of increase/decrease. When solving for percent of increase or decrease, the whole is always the original value or value before the change occurred. The part is the change in values, that is, how much something went up or went down. Example: a) As first public inquiry showed, there were 633,000 women motorcyclists in the United States, up from 443,000 just eight years before it. Find the percent of increase in the number of women motorcyclists during these eight years. b) College students are offered an 8% discount on a textbook that sells for $ If the sales tax is 8%, find the cost of the textbook including the sales tax. c) What is the total price of a boat with an original price of $12,685, if it is sold at a 15% discount? The sales tax rate is %.

3 MATH 1012 Section 6.7 Simple Interest Bland Interest is a fee paid or a charge made for lending or borrowing money. The amount of money borrowed is called the principal. The charge for interest is often given as a percent, called the interest rate of rate of interest. The rate of interest is assumed to be per year, unless stated otherwise. Time is always expressed in years or fraction of a year. Formula for Simple Interest The formula is usually written using letters. a) Find the interest of $5000 at 6% for 2 years. The amount borrowed, or principal (p), is $5000. The interest rate (r) is 6%, which is 0.06 as a decimal, and the time of the loan (t) is 2 years. Use the formula. The interest is $600. b) Find the interest on $4200 at 8% for three and a half years. c) Find the interest on $840 at for 9 months. When a loan is repaid, you have to repay the original amount borrowed plus the interest. Formula for Amount Due In examples a, b, and c find the amount due.

4 MATH 1012 Section 6.8 Compound Interest Bland The interest we studied in Section 6.7 was simple interest (interest only on the original principal). A common type of interest used with savings accounts and most investments is compound interest or interest paid on past interest as well as on the principal. Suppose that you make a single deposit of $1000 in a savings account that earns 5% per year. What will happen to your savings over 3 years? At the end of the first year, 1 year s interest on the original deposit is found. Use the simple interest formula. Formula for Simple Interest Year 1 ($1000)(0.05)(1) =$50 Add the interest to the $1000 to find the amount in your account at the end of the first year. $ $50 =$1050. The interest for the second year is found on $1050; that is, the interest is compounded. Year 2 ($1050)(0.05)(1)=$52.50 Add this interest to the $1050 to find the amount in your account at the end of the second year. $ $52.50 =$ The interest for the third year is found on $ Year 3 ($ )(0.05)(1) $55.13 Add this interest to the $ So, $ $55.13 = $ At the end of three years, you will have $ in your savings account. The $ that you have in your account is called the compound amount. To find the Compound interest we subtract our compound amount from the principal. The compound interest was $

5 MATH 1012 Section 6.8 Compound Interest Bland Example Nancy Wegener deposits $3400 in an account that pays 6% interest compounded annually for 4 years. Find the compound amount. Round to the nearest cent, when necessary. This problem is solved three ways. 1) Make a Chart Method Year Interest Compound Amount $ $ $ The Compound amount after 4 years is $ ) Multiplication Method This is a more efficient way of finding the compound amount. Usually used with a calculator. We will add 100% to the interest rate. Then multiply by the original deposit. Interest rate is 6% so, adding 100% we get 106% or 1.06 as a decimal. Year 1 Year 2 Year 3 Year 4 Original Deposit Compound Amount The compound amount is $

6 MATH 1012 Section 6.8 Compound Interest Bland 3) Compound Interest Table A compound interest table is the easiest method. You take the principal and multiply by the appropriate value on the chart. So, given the chart below we will select the value that is in the cross-section of 4 years and 6%. Time Periods 3.00% 3.50% 4.00% 4.50% 5.00% 5.50% 6.00% 8.00% Time Periods At the intersection of 4 years and 6% we get We will multiply this to our principal. The compound amount is $ Note: This answer is not the same as our previous answers. This is due to the rounding of the values in the table. Because of this, be sure to use whichever method is asked for in the problem. Extra Information: Some tables are more precise and would have given us instead of Using this number then rounding to the nearest cent would be: Which would match our previous values.