1. Financial Math Currency, Interest and Depreciation Mr. Morrow 2/21/2013 – 2/26/2013

2. - Warm Up - Suppose one night you go out to dinner downtown. The sales tax on food is 5.02%. The final bill (before tip) came to 52.43. How much was your dinner before tax? Two baseball players, A and B, are in their first half of the season. Player A’s batting average was higher than play B’s batting average. During the second half of the season, player A’s batting average was higher than player B’s (again). For the entire season, player B’s batting average was higher than that of player A. Is that possible? Assume it takes 6 hours to fully cook your 8lb Thanksgiving turkey. You only have 253 minutes that you can set aside to cook though. How much turkey should you get if that is all of the time you have?

3. - Warm Up - Player A Player B 1st Half 3 hits/9 at bats> 3 hits/10 at bats 2nd Half1 hit/1 at bat> 7 hits/10 at bats Whole Season4 hits/10 at bats< 10 hits/20 at bats

4. - Currency Conversion - Well we all saw last week that: 1 = 1 So can anyone explain to me how this can actually be true…?? 1 ≠ 1 … $1 ≠ € 1 Yea it couldn’t have anything to do with the big heading at the top…Currency Several aspects affect the conversion rate between countries: Buying/ Selling Investments in various countries Strength/ Success of country’s economy But this is economics, who wants to learn about that in a Math class……

5. - Currency Conversion - For this section we will be looking at the idea of, Exchange rates- The price of one country's currency expressed in another country's currency. In other words, the rate at which one currency can be exchanged for another. Foreign Currency Exchange Rate CurrencyWe Buy We Sell Currency We Buy We Sell USD1.6321.494 EUR 1.2071.106 AUD1.8391.660 CAD1.7241.549 CZK31.20827.645 DKK9.0268.072 JPY150.853134.585 NZD2.3632.113 PLN4.8764.299 NOK9.8268.787 ZAR12.59311.208 SEK11.94710.683 CHF1.7771.589 TRY2.4952.227 AED6.0215.410 How many UK pounds ( £) will you get for your $150?

6. - Currency Conversion -

7. - Practice - Assume the currency conversion rates between the US and four countries are shown below: US ($) Aus ($A) Sterling (£) Yen (¥) Euro (€) 1 1.633 0.610 134.490 1.352 Convert: 1.$50 US to Yen 2.£15 to $US 3.$1500 Australian to Euro 4.¥125 to Sterling

8. - Practice -

12. - A Case of Robbery -

13. - Commission -

14. - Practice -

15. - Walk Out…and take home to finish - Suppose you are planning your honeymoon and need to determine how much money you are going to spend for the entire trip. Fill in the blanks to the following ‘Trip Scenario’ then determine the cost of your Honeymoon. Sunday night we are leaving from Dulles Airport to _________. The flight is going to cost $2,500 USD. We are going to stay there for 2 nights at their Trump Hotel which has breakfast, lunch and dinner included in the cost for __ 500. The next morning we are planning to rent a car for __ 750 (Assume no gas purchases). We drive from _________ to _________ where we will stay at their Hilton for one night at __ 150. Wednesday morning we board a flight from _________ to _________ for __ 3,250. Being the last stop on our trip we want this to be really memorable. We take a guided tour of the area for __ 100, buy __ 350 worth of souvenirs, partake in __ 1,200 worth of activities, and our romantic meals for those 2 days add up to __ 800. Our flight home Saturday morning costs __ 3,250.

16. - Exchange Rates (2/8/13) - We BuyWe Sell US $ 1.63 1.49 €-Euro1.211.11 British Pound-£9.618.73 Canadian $1.721.55 Australian $1.841.66 Indian Rupee44.541.4 Philippine Peso57.453.7 Swiss Franc1.781.59 South African Rand12.611.2 New Zealand $2.362.11 Jamaica $137.1132.4 Japanese Yen150.9134.6 Russian Ruble44.139.8 Brazilian Real2.882.63 ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙

17. - Warm Up - A bank offers the following exchange rates for 1 German mark in relation to the European Euro: ‘We Buy: 1033, we sell:1019’. If a customer wishes to exchange the following amounts, find: 1.The number of Euros the customer receives, correct to the nearest number. 2.The number of German marks that will result if the amount in i. is immediately returned to German marks. 3.The effective commission on the two transactions. a) (1000)b) (1608)c) (1217)

18. - Interest -

20. - Practice -

21. - Simple (Graphically) - Simple interest is the most basic type of return. Suppose we deposit $100 into an account with 50% simple (annual) interest, we could represent it like this: You start with a principal of $100 and earn $50 each year. However this ‘new’ green money is stagnant – it can’t grow! With simple interest, the $50 just sits there. Only the original $100 can do ‘work’ to generate money For simple interest you can kind of imagine It as ‘speed’. Here you’ll earn 50% of your Principal in the course of a year. (your ‘speed of money growth’).

22. - Compound Interest -

23. - Practice -

24. - Compound (Graphically) - Simple interest should make you squirm. Why can’t our interest earn money? We should use the bond payouts ($50/year) to buy more bonds. Compound growth means your interest earns interest. Einstein called it “one of the most powerful forces in nature”, and it’s true. When you have a growing thing, which creates more growing things, which creates more growing things… your return adds up fast. We earn $50 from year 0 – 1, just like with simple interest. But in year 1-2, now that our total is $150, we can earn $75 this year (50% * 150) giving us $225. In year 2-3 we have $225, so we earn 50% of that, or $112.50. This is an interesting viewpoint. The $100 just mindlessly cranks out $50 “factories”, which start earning money independently (notice the 3 blue arrows from the blue principal to the green $50s). These $50 factories create $25 factories, and so on. The pattern seems complex, but it’s simpler in a way as well. The $100 has no idea what those zany $50s are up to: as far as the $100 knows, we’re only making $50/year. With simple interest, we kept the same pace forever ($50/year — pretty boring). With annually compounded interest, we get a new trajectory each year.

25. - Compound-(ing) Interest -

26. - Practice -

27. - Effective Interest Rates -

28. - What is time, time, time, baby just solve for me once more -

29. - Practice -

30. - Warm Up - $2,500 is placed in a savings account that pays 6.5% interest compounded monthly. Find the amount in the account and the interest paid after 20 years. How much interest was actually earned? If $500 is invested in an account and earns $75.50 simple interest over 2.75 years, find the annual interest rate and future value. How long will it take $2,000 to grow to $4,300 if invested at 8% with interest compounded quarterly?

31. - Depreciation -

32. - Flat Rate (Straight-line) - What do you think this section of deprecation relates to in what we’ve been learning about? ∙ Arithmetic Growth (Straight-line function) If an asset's value declines at a fixed rate over time then it is said to experience straight line or flat rate depreciation. Original Cost of Asset (Purchase Price) C Book Value ($) BV t Time t (periods) Time until the asset is written off BV t T Book value at time T = t BV t = C – Rt (Where R is the fixed rate of depreciation)

33. - Practice -

35. - Reducing Balance -

36. BV t t C Scrap value Book value at time T T BV t

37. - Practice - Glen Allen towing just bought two new tow trucks for $35,000 each. They decide that one of the trucks will be depreciating at the flat rate of 15% of the purchase price, while the other will be depreciating at 20% using a reducing balance method. It is estimated that the trucks will have a useful life of 6 years. 1. Construct a depreciation schedule for each truck 2. Sketch the graphs showing the relationship between the truck’s book value and the time since they were purchased. 3. At the end of 6 years, Glen Allen towing analyzes the depreciation behavior for both methods. Is there a preference as to which method they should use in the future?

38. - Practice - Year1st Truck2nd Truck 0$35,000 1$29,750$28,000 2$24,500$22,400 3$19,250$17,920 4$14,000$14,336 5$8,750$11,469 6$3,500$9,175 Reducing balance Flat rate Book value is equal 12 3 4 5 6

39. - Unit Cost -

40. - Practice -

41. Our $120,000 Audi has a scrap value of $25,000 once we have driven 250,000 miles. 1. Find the depreciation rate in dollars/ km 2. Find the book value of the car after reaching 50,000 miles Homework: pg. 664 – Grade Revision Exercises (All)

42. - Practice -