1. Sales tax, simple interest, and compound interest. FINANCES PART I

2. SALES TAX Optional for individual states. How to compute sales tax: (Total cost of item) x (percent of sales tax) = amount of sales tax Cost of item + amount of sales tax = register price If we put these two equations together and factor we can get: Cost of item + cost of item x percent of sales tax = register price Cost of item x (1 + percent of sales tax) = register price

3. SALES TAX EXAMPLES You find the perfect throw rug in Walmart for $19.88. You are in an area that charges 6% sales tax. How much will you actually pay for the rug? You see an HP laptop at Staples that you just have to have. The listed price is $899.99. If the sales tax rate is 7.25%, how much will you pay for your new computer?

4. SALES TAX SOLUTIONS You find the perfect throw rug in Walmart for $19.88. You are in an area that charges 6% sales tax. How much will you actually pay for the rug? The throw rug costs 19.88, we multiply that by the tax rate in decimal form: 19.88 x 0.06 = 1.1928. As we are talking about money, we always round to two decimal places. We now have a tax amount of $1.19. The question asks for how much we actually pay so we add the price of the rug plus the amount of tax to find 19.88 + 1.19 = $21.07 at the register. NOTE: If we take the price of the rug (which is a 1) and the percentage of tax (which is 0.06) and add these together, we can find the register price by 19.88 x 1.06 = 21.07. This is a much faster way of doing the calculation

5. SALES TAX SOLUTIONS You see an HP laptop at Staples that you just have to have. The listed price is $899.99. If the sales tax rate is 7.25%, how much will you pay for your new computer? The HP is 899.99. With tax at 7.25% we can find the register price to be 899.99 x (1 + 0.0725) = 899.99 x 1.0725 = $965.24.

6. SIMPLE INTEREST Simple interest is just an extension of sales tax. Simple interest formula: Simple interest = (Principal) x (rate) x (time). The principal is the amount of the loan. The rate is always computed as a decimal, never as a percentage. The time is always given in years so sometimes we need to convert from months to years.

7. SIMPLE INTEREST EXAMPLES I borrow $500 for 1 year at a simple interest rate of 4%. How much interest accumulates over that time? How much would I have to repay in total? I borrow $4000 from my mom and plan to repay it in 3 years. If she charges me 2% interest, how much would I owe mom at the end of the time period?

8. SIMPLE INTEREST SOLUTIONS I borrow $500 for 1 year at a simple interest rate of 4%. How much interest accumulates over that time? How much would I have to repay in total? With P = 500, t = 1 year, and r = 4% = 0.04, we find the simple interest to be: INT = 500 x 0.04 x 1 = $20. This is the amount of interest that accumulates. As this is a loan, we must repay the original $500 plus the amount of interest, $20, for a total of $520 repaid.

9. SIMPLE INTEREST SOLUTIONS I borrow $4000 from my mom and plan to repay it in 3 years. If she charges me 2% interest, how much would I owe mom at the end of the time period? With P = 4000, t = 3 years, and r = 2% = 0.02, we find INT = 4000 x 0.02 x 3 = $240. This means I must repay a total of $4240, with $240 of it being interest.

10. MORE SIMPLE INTEREST EXAMPLES Suppose you invest $1000 in a savings bond that pays 10% simple interest per year. How much total interest will you receive in 5 years? You deposit $2500 in an account that pays you simple interest of 3.2% per year. How much will you have in the account in 18 months?

11. MORE SIMPLE INTEREST SOLUTIONS Suppose you invest $1000 in a savings bond that pays 10% simple interest per year. How much total interest will you receive in 5 years? Here we have P = 1000, r = 10% = 0.10, and t = 5 years. Then INT = 1000 x 0.10 x 5 = $500. We will have $500 in total interest on this investment.

12. MORE SIMPLE INTEREST SOLUTIONS

13. COMPOUND INTEREST Compound interest is interest that accrues on the initial principal and the accumulated interest of a principal deposit, loan or debt. Compounding of interest allows a principal amount to grow at a faster rate than simple interest.

14. ACCORDING TO INVESTOPEDIA The more frequently interest is added to the principal, the faster the principal grows and the higher the compound interest will be. The frequency at which the interest is compounded is established at the initial stages of securing the loan (or opening the account).

15. COMPOUND INTEREST VIDEO

16. COMPOUND INTEREST FORMULA

17. COMPOUND INTEREST EXAMPLES 1.Suppose I invested $10,000 at an APR of 4% for 10 years with annual compounding. How much would I have at the end of the term? 2.Suppose I invested $10,000 at an APR of 4% for 10 years with monthly compounding. How much more would I have than with annual compounding? 3.Suppose I invest $2000 for 5 years with an APR of 3% and daily compounding. How much would I have at the end of the term?

18. COMPOUND INTEREST SOLUTIONS

21. HOMEWORK You now have the tools with which to complete problems 1.1 through 1.7 in Jack Appreciates Math chapter one.