2. Aim: Simple Interest Course: Math Literacy Aim: How to get our money to grow? Do Now: At a Forest Service Youth Camp many of the workers ate some meals away from the base camp. In the dining hall at the base camp, 5% of the workers had breakfast only, 3% had lunch only, and 2% had supper only. Just 10% of the workers ate all three meals in camp. There were 5000 meals served at the base camp dining hall. No worker missed all three meals. How many workers were assigned to the Youth Camp?

3. Aim: Simple Interest Course: Math Literacy At a Forest Service Youth Camp many of the workers ate some meals away from the base camp. In the dining hall at the base camp, 5% of the workers had breakfast only, 3% had lunch only, and 2% had supper only. Just 10% of the workers ate all three meals in camp. There were 5000 meals served at the base camp dining hall. No worker missed all three meals. How many workers were assigned to the Youth Camp? Let x = the number of workers (.05) x = # eating breakfast only (.03) x = # eating lunch only (.02) x = # eating supper only (.10) x = # eating 3 meals (.80) x = # eating 2 meals 1(.10x) + 3(.10x) + 2(.80x) = 5000 2x = 5000 x = 2500 Model Problem

4. Aim: Simple Interest Course: Math Literacy A jacket regularly sells for $135. The sale price is $60.75. Find the percent decrease of the sale price from the regular price. Finding Percent Increase or Decrease 1)Find the fraction for the percent increase or decrease. 1)Find the percent increase or decrease by expressing the fraction in step 1 as a percent

5. Aim: Simple Interest Course: Math Literacy Simple Interest – Money in the Bank Annie deposits $1000 in a local bank at 8% interest for 1 year. How much does Annie earn after 1 year? 1000 + 1000(0.08)(1) = $1080 P= A - End of year balance + Prt = 1000(1.08) Accumulated Amount (A) – total amount yielded after an amount of time t usually a year, also called Future Value Principal (P) – initial amount invested/deposited or Present Value Interest (I) – amount earned for t period I = PrtA = P + I = P + Prt = P(1 + rt) = P(1 + rt)

6. Aim: Simple Interest Course: Math Literacy = A - End of 2 years Simple Interest – Money in the Bank Annie deposits $1000 in a local bank at 8% interest for 1 year. How much does Annie earn after 2 years? 1000 + 1000(0.08)(2) = $1116 P + Prt = 1000(1.16) = P(1 + rt) Accumulated Amount (A) – total amount yielded after an amount of time t usually a year, also called Future Value Principal (P) – initial amount invested/deposited or Present Value Interest (I) – amount earned for t period I = PrtA = P + I = P + Prt = P(1 + rt)

7. Aim: Simple Interest Course: Math Literacy Definition of Arithmetic Sequence A sequence is arithmetic if the differences between consecutive terms are the same. Sequence a 1, a 2, a 3, a 4,..... a n,... is arithmetic if there is a number d such that a 2 – a 1 = d, a 3 – a 2 = d, a 4 – a 3 = d, etc. The number d is the common difference on the arithmetic sequence. Each term after the first is the sum of the preceding term and a constant, c. 7, 11, 15, 19,.... 4 4 4 4 = d 2, -3, -8, -13,.... -5 -5 -5 -5 = d 4n + 3,... 7 – 5n,... finite infinite 1 st termn th term

8. Aim: Simple Interest Course: Math Literacy The n th Term of an Arithmetic Sequence The n th term of an arithmetic sequence has the form a n = dn + c where d is the common difference between consecutive terms of the sequence and c = a 1 – d An alternative form of the n th term is a n = a 1 + (n – 1)d A = P + Prt = P(1 + rt) Arithmetic growth (linear growth) – growth by a constant amount in each time period. 16 = 4 + (5 – 1)3 a n = 3n + 1 A = 100(1 + rt) 110 = 100(1 +.10(1)) 120 = 100(1 +.10(2)) 160 = 100(1 +.10(6))

9. Aim: Simple Interest Course: Math Literacy Model Problem A loan of $1060 has been made a 6.5% per year for three months. Find the loan’s future value? = A - End of 3 months 1060 + 1060(0.01625) = $1077.23 P + Prt 3 months is ¼ of a year ¼ of 6.5% =.25 of 0.065 = 0.01625 A = P + I = P + Prt = P(1 + rt)

10. Aim: Simple Interest Course: Math Literacy Model Problem You borrow $2500 from a friend and promise to pay back $2655 in six months. What simple interest rate will you pay? 6 months is ½ or 0.5 of a year = A 2500(1 + r(0.5)) = 2655 P(1 + rt) A = P + I = P + Prt = P(1 + rt) 2500 + 2500r(0.5) = 2655 1250r = 155 r = 0.124 = 12.4%

11. Aim: Simple Interest Course: Math Literacy Model Problem If $10,000 is deposited in an account earning 5¼ % simple interest, what is the future value in 5 years? P = 10,000 r =.0525 A = $12,875 A = P + I = P + Prt = P(1 + rt)

12. Aim: Simple Interest Course: Math Literacy Model Problem You plan to save $2000 for a trip to Europe in two years. You decide to purchase a certificate of deposit (CD) from your bank that pays a simple interest rate of 4%. How much must you put in this CD now in order to have $2000 in two years? = A P(1 + (0.04)(2)) = 2000 P(1 + rt) A = P + I = P + Prt = P(1 + rt) P + P(0.08)= 2000 1.08P = 2000 P = $1851.852

13. Aim: Simple Interest Course: Math Literacy Discounted Loan Discounted Loan – A loan where the interest to be paid for the loan is collected when the loan is made. Discount – the interest amount that is deducted from the loan initially. You borrow $10,000 on a 10% discounted loan for a period of 8 months. a)What is the loan’s discount? b)Determine the net amount of money you receive. c)What is the loan’s actual interest rate?

14. Aim: Simple Interest Course: Math Literacy Model Problem You borrow $10,000 on a 10% discounted loan for a period of 8 months. a)What is the loan’s discount? b)Determine the net amount of money you receive. c)What is the loan’s actual interest rate? I = Prt I = 10,000(.10)(2/3)= 666.67a) 10,000 – 666.67 = 9333.33b) c)666.67 = 9333.33(r)(2/3) r = 0.107 → 10.7%

15. Aim: Simple Interest Course: Math Literacy Model Problem You borrow $1200 on March 25 at 21% simple interest. How much interest accrues to September 15 (174 days later)? What is the total amount that must be repaid? P = 1200 r =.21 I = Prt A = P + I A = 1200 + 121.80 = 1321.80