Maths In The Real World

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This document contains examples and problems related to percentages, ratios, proportions, area, plans and elevations, word problems involving equations, and currency conversions. It covers topics like calculating earnings and savings over time, determining materials needed for construction projects, solving retail scenarios involving customers and commissions, and designing geometric patterns. The document provides practice for bridging math skills from key stage 3 to key stage 4.

Maths in the Real World KS3 to KS4 Bridging Unit June 2008

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Question 1. You can earn $40 in interest on a $1,000 deposit for 8 months. If the EAR is the same regardless of the length of the investment, how much interest will you earn on a $1,000 deposit for: a. 2 months. b. 1 year. c. 1.5 years. a. 2-months. For a 2-month, $1,000 deposit you will earn $. (Round to the nearest cent). b. 1-year. For a 1-year, $1,000 deposit you will earn $. (Round to the nearest cent). c. 1.5-years. For a 1.5-year, $1,000 deposit you will earn $. (Round to the nearest cent). Question 2. You have decided to refinance your mortgage. You plan to borrow whatever is outstanding on your current mortgage. The current monthly payment is $3,053 and you have made every payment on time. The original term of the mortgage was 30 years, and the mortgage is exactly four years and eight months old. You have just made your monthly payment. The mortgage interest rate is 5.798% (APR). How much do you owe on the mortgage today? The amount you owe today is $. (Round to the nearest dollar.) Question 3. Consider a project that requires an initial investment of $100,000 and will produce a single cash flow of $150,000 in 5 years. a. What is the NPV of this project if the 5-year interest rate is 5.0% (EAR)? b. What is the NPV of this project if the 5-year interest rate is 10.0% (EAR)? c. What is the highest 5-year interest rate such that this project is still profitable? a. What is the NPV of this project if the 5-year interest rate is 5.0% (EAR)? The NPV in this case (EAR equals 5.0 %) is $. (Round to the nearest dollar.) b. What is the NPV of this project if the 5-year interest rate is 10.0% (EAR)? The NPV in this case (EAR equals 10.0 %) is $. (Round to the nearest dollar.) c. What is the highest 5-year interest rate such that this project is still profitable? The highest EAR such that this project is still profitable is % (Round to two decimal places.) Question 4. In the summer of 2008, at Heathrow airport in London, Bestofthebest (BB), a private company, offered a lottery to win a Ferrari or 87,000 British pounds, equivalent at the time to about $174,000. Both the Ferrari and themoney, in 100 pound notes, were on display. If the U.K. interest rate was 4% per year, and the dollar interest rate was 2% per year (EARs), how much did it cost the company in dollars each month to keep the cash on display? That is, what was the opportunity cost of keeping it on display rather than in a bank account? (Ignore taxes.)Hint: Make sure to round all intermediate calculations to at least five decimal places. The opportunity cost of keeping it on display rather than in a bank account is £ per month. (Round to two decimal places). Question 5. A 30-year bond with a face value of $1,000 has a coupon rate of 5.50%, with semiannual payments. a. What is the coupon payment for this bond? b. Enter the cash flows for the bond on a timeline a. What is the coupon payment for this bond? The coupon pay ...

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