Aim: Simple Interest Course: Math Literacy Aim: How to get our money to grow? Do Now: At a Forest...

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?


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) = 50002x = 5000 x = 2500

Model Problem


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

135.00 60.65

135.00

Finding Percent Increase or Decrease1) 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

amount of increase or decrease

original amount

135.00 74.25

135.00

.55 55%


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 ValuePrincipal (P) – initial amount invested/deposited or Present ValueInterest (I) – amount earned for t period

I = Prt A = P + I = P + Prt = P(1 + rt)= P(1 + rt)


= 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 ValuePrincipal (P) – initial amount invested/deposited or Present ValueInterest (I) – amount earned for t period

I = Prt A = P + I = P + Prt = P(1 + rt)


Definition of Arithmetic Sequence

A sequence is arithmetic if the differences between consecutive terms are the same. Sequence

a1, a2, a3, a4, . . . . . an, . . .

is arithmetic if there is a number d such that

a2 – a1 = d, a3 – a2 = d, a4 – a3 = 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

1st term nth term


The nth Term of an Arithmetic Sequence

The nth term of an arithmetic sequence has the form

an = dn + c

where d is the common difference between consecutive terms of the sequence and

c = a1 – d

An alternative form of the nth term is an = a1 + (n – 1)d

A = P + Prt = P(1 + rt)

Arithmetic growth (linear growth) – growth by a constant amount in each time period.

16

14

12

10

8

6

4

2

5 10 15

F: (5.00, 16.00)

D: (4.00, 13.00)

C: (3.00, 10.00)

B: (2.00, 7.00)

A: (1.00, 4.00)

h x = 3x+1

16 = 4 + (5 – 1)3

an = 3n + 1

200

180

160

140

120

100

80

60

40

20

2 4 6

N: (0.00, 100.00)M: (1.00, 110.00)

L: (2.00, 120.00)K: (3.00, 130.00)

J: (4.00, 140.00)

I: (5.00, 150.00)H: (6.00, 160.00)

A = 100(1 + rt)

g x = 10x+100

110 = 100(1 + .10(1))

120 = 100(1 + .10(2))

160 = 100(1 + .10(6))


Model Problem

A loan of $1060 has been made a 6.5% peryear for three months. Find the loan’s futurevalue?

= 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)


Model Problem

You borrow $2500 from a friend and promiseto pay back $2655 in six months. What simpleinterest 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%


Model Problem

If $10,000 is deposited in an account earning 5¼ % simple interest, what is the future value in 5 years?

5t P = 10,000 r = .0525

10000(1 0.0525(5))A

A = $12,875

A = P + I = P + Prt = P(1 + rt)


Model Problem

You plan to save $2000 for a trip to Europe intwo years. You decide to purchase a certificateof deposit (CD) from your bank that paysa simple interest rate of 4%. How muchmust 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


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?


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%


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?

174

360t P = 1200 r = .21

I = Prt

1741200(.21) 121.80

360I

A = P + I

A = 1200 + 121.80 = 1321.80

Aim: Simple Interest Course: Math Literacy Aim: How to get our money to grow? Do Now: At a Forest...

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