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**Do now – grab a calculator**

What is the simple interest formula? What is the meaning of each variable in the future value formula?

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Homework ?’s Page 637 #’s 7 – 15 odd

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**11.2 Interest Goals: Understand simple interest formula.**

Use the compound interest formula.

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Present Value Present value – the amount you have to invest in an account now to have a specified amount in the account in the future.

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Example #1 Assume you need to save $2,500 to take a trip in two years. Your bank offers a CD that pays 4% annual interest. How much must you put in this CD now to have the money needed in two years?

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**Example #1 A = P(1 + rt) 2500 = P(1 + 0.04 x 2) 2500 = P (1.08)**

We would have to round this value up to $ so you would be guaranteed to have the amount needed. Now you try problem #2

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Compound Interest Compound Interest – interest that is paid on principal plus previously earned interest.

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Compound Interest A = future value P = principal r = interest rate as a decimal n = times per year the interest is compounded, t = time in years

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Compound Interest Compounded annually – interest that is added one time each year. Compounded semi-annually – interest that is added two times a year. Compounded quarterly – interest that is added 4 times a year. Compounded monthly – interest that is added 12 times a year. Compounded daily – interest that is added 365 times a year.

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Example #3 You deposit $2,000 in a bank account that pays 10% annual interest, compounded annually. How much will be in the account at the end of three years?

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Example 3 You deposit $2,000 in a bank account that pays 10% annual interest, compounded annually. How much will be in the account at the end of three years?

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Example #3 You deposit $2,000 in a bank account that pays 10% annual interest, compounded annually. How much will be in the account at the end of three years? Compare that to the amount that would be in the account if the bank used the simple interest formula?

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You Try: Examples 4&5 4. You put $10,000 in a 5 year CD. The interest rate is 5% compounded quarterly. How much money will you have in 5 years? 5. You put $10,000 in a 5 year CD. The interest rate is 4.8% compounded monthly. How much money will you have in 5 years?

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What is a CD? A certificate of deposit (CD) is a time deposit, a financial product commonly sold in the United States by banks, thrift institutions, and credit unions.

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Example 6 As a parent you’ll want to make a deposit into a tax-free account to use later for their college education. Assume that the account has an annual interest rate of 8% compounding yearly. How much must you deposit now so that you’ll have enough by the time your child is 18? College cost in 2030

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Interest rate? Example 7 Suppose you are looking to invest $2,000 and you need to have a minimum of $2500 in 3 years. You found an account that compounds interest annually, what is the minimum interest rate necessary?

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**How long will it take? Example 8**

Suppose you want to buy something for $1,500. You presently have $1,000 in a CD that has 4% annual interest, compounded annually. How many years will it take for you to save enough money?

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**The exponent property of the log function**

“log” or “log x” stands for the common logarithmic function. We can use it to solve for nt in the formula A=P(1 + r/n)nt. log yx = x log y

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Solve for x using logs 3x = 10 (1.05)x = 2 X3 = 10

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Example 8 1,500 = 1,000( /1)1·t 1,500 = 1,000(1.04)t 1.5 = 1.04t log 1.5 = log 1.04t log 1.5 = t log 1.04 t = log 1.5/log 1.04 t = 10.34

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Do NOW Textbook page 637 #’s 26, 28, 32, 44, 48

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**Do NOW - ANSWERS Textbook page 637 #’s 26, 28, 32, 44, 48 $9,014.60**

$13, 4.75% compounded monthly 9.65% 15.73%

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**Homework HW – pg 636 #’s 23 – 57 odd Extra Credit worksheet**

Answer true or false questions about credit cards.

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Preview of tomorrow Compute finance charges for credit cards using 2 methods. Compute monthly payments for installment loans.

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**11.3 Consumer loans and credit cards**

Objectives: Determine payments for an add-on loan. Compute finance charges on a credit card using the unpaid balance method Use the average daily balance method to compute credit card charges Compare credit card finance charge methods

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**How are you going to pay for that?**

Debt Trap

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**Closed-ended credit Installment Loans**

Installment loans – loans having a fixed number of payments Installment – the payments made on a loan. Finance charge – interest charges on a loan.

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Determining Payments Example 1: you decided to purchase an Ipad 3 64 MB with the black leather cover for $ You intend to take out an installment loan for 2 years at an annual interest rate of 18%. If the store is using the add-on interest method, what will be your monthly payments?

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**Installment Loan Monthly payment = P + I n P : the loan amount,**

I: is the amount of interest due on the loan, n: is the number of monthly payments You try #’s 7 & 11 page 646

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**Credit Card Finance Charges**

Unpaid balance method – interest is based on the previous month’s balance. Average daily balance method – (most common) balance is the average of all daily balances for the previous month.

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Unpaid Balance Method Assume that the annual interest rate on your credit card is 18% and your unpaid balance at the beginning of last month was $600. Since then, you purchased ski boots for $130 and sent in a payment of $170. Using the unpaid balance method: a. what is your credit card bill this month? b. what is your finance charge next month?

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**Unpaid balance method for computing the finance charge on a credit card**

Note: This method also uses the simple interest formula I = Prt; however P = the previous month’s balance + finance charge + purchases made - returns - payments r = interest rate t = 1/12

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**Unpaid Balance Method Previous month’s balance = 600**

Finance charge on last month’s balance = 600(0.18)(1/12) = $9 Purchases made = 130 Returns = 0 Payment = 170 So P = – 0 – 170 = 569 (this month’s bill) The finance charge for next month will be I = Prt = 569(0.18)(1/12) = 8.54

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Quiz Yourself Assume that the annual interest rate on your credit card is 21%. Your outstanding balance last month was $300. Since then you have charged a $84 purchase and made a $100 payment. a. What is the outstanding balance on your card at the end of the month? b. What is next month’s finance charge on this balance?

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Quiz Yourself Assume that the annual interest rate on your credit card is 21%. Your outstanding balance last month was $300. Since then you have charged a $84 purchase and made a $100 payment. a. What is the outstanding balance on your card at the end of the month? $289.25 b. What is next month’s finance charge on this balance? $5.06 You try: #25

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**Paying off credit card debt**

Assume that you have a credit card debt of $6589 and you are making the minimum $100 monthly payment. Assume the annual interest rate is 18% and the credit card company is using the unpaid balance method to compute your finance charges. What will your balance be at the end of one month? How much did you actually reduce your dept?

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Ask yourself How can you use the unpaid balance method to your advantage?

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**Average Daily Balance Method**

The balance is the average of all daily balances for the previous months Note: this is the most commonly used method for determining finance charges.

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**Average Daily Balance Example 3 :**

Suppose that you begin the month of September (30 days) with a credit card balance of $240. Your card has an annual interest rate of 18% during September you had the following adjustments to your account: 9/13 You made a payment of $60 9/18 a charge of $24 9/23 a charge of $12 Use the average daily balance method to compute the finance charge that will appear on your October statement.

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**Average Daily Balance Method**

Add the outstanding balance for your account for each day of the month. Divide the total in step 1 by the number of days in the month to find the average daily balance To find the finance charge use the formula I=Prt where: P = the average daily balance r = the annual interest rate t = # of days in the month divided by 365

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**Solution Day Balance # of days x balance 1-12 $240 12 x 240 = 2,880**

13-17 $180 5 x 180 = 900 18-22 $204 5 x 204 = 1,020 23-30 $216 8 x 216 = 1,728 The average daily balance is: 2, , , = 30 We next apply the simple interest formula: I = (0.18)(30/365) = 3.22 So the finance charge will be $3.22

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Quiz Yourself Recalculate the average daily balance in the previous example, except now assume you spent the $24 on September 3rd instead of the 18th. Make a table. You try # 29.

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Comparing methods Suppose that you begin the month of May (31 days) with a credit card balance of $500. The annual interest rate is 21%. The following adjustments were made: 5/11 you charge $400, 5/29 you make a payment of $500. Calculate the finance charge that will be on the next statement using the two methods.

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**Solution Method= P r t Finance charge I=Prt Unpaid balance**

Average daily balance

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**Solution Method P r t Finance charge I=Prt Unpaid balance**

Last month’s balance + finance charge – payment + charges = – 500 = 21% 1/12 (408.75)(0.21)(1/12) = $7.15 Average daily balance

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**Solution Method P r t Finance charge I=Prt Unpaid balance**

Last month’s balance + finance charge – payment + charges = – 500 = 21% 1/12 (408.75)(0.21)(1/12) = $7.15 Average daily balance (10 x 500) + (18 x 900) + (3 x 400) = 31 31/365 (722.58)(0.21)(31/365) = $12.89

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**What have you learned Answer the following questions:**

Describe how we calculated the the payments for the add-on interest loan in Example 1. In example 2, we computed the finance charge from the previous month using the expression Prt, what does each variable represent. How can you use the unpaid balance method to your advantage?

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Class work Page 646 – 648 #’s 12, 24, 30, 34

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Homework 11.1 – 11.3 Take home quiz

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Chapter 5 Mathematics of Finance

Chapter 5 Mathematics of Finance

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