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Mortgages and Investments:

Using Exponential Equations to Solve Financial Problems

One application of strong math skills is in the world of finance. Whether you are giving advice, designing your own financial future, or simply making short-goal decisions about your money, math is almost always a concern. Exponential equations model many financial situations, including the purchase of a house and building wealth in an investment. In this mini-project, you will be exploring different aspects of these two situations.

TASK ONE: Researching a home.

You may have dreams of one day owning your own home. Perhaps you have seen many mansions on MTV’s Cribs, and you would like to know more about the costs involved in owning such a home. Most successful adults want to invest in a home, and their expectations of that home are varied. To get started, we will research, via the internet, several personal options of the home we might want to invest in.

• Use the website, , to find 3 different homes for sale. List the prices and some of the home’s desirable attributes (i.e. location, amenities, price, etc.)

|Home Address: | | | |

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|List Price: | | | |

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TASK TWO: Calculating monthly payments.

Lenders offer loans with terms that differ based on interest rates and “points.” A point is a fee that equals 1% of the loan amount and must be paid up front. Lenders typically offer loans of the same type that differ based on the number of points and interest rates. To compare similar loans, you must consider interest rates and upfront costs such as points. Suppose a lender offered 30-year conventional loans with the following conditions:

|Loan |Annual Interest Rate (APR) |Points |

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|Loan A |6.25% |4.00 |

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|Loan B |6.50% |2.75 |

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|Loan C |6.75% |1.75 |

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|Loan D |7.25% |0.00 |

To calculate the “down payment” you must use the points of each loan and calculate the percentage of the asking price that you will have to pay. Calculate the down payments for each house:

| |House #1 |House #2 |House #3 |

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|Loan A | | | |

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| |Down Payment = ___________ |Down Payment = ___________ |Down Payment = ___________ |

| |Amt to Borrow = ___________ |Amt to Borrow = ___________ |Amt to Borrow = ___________ |

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|Loan B | | | |

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| |Down Payment = ___________ |Down Payment = ___________ |Down Payment = ___________ |

| |Amt to Borrow = ___________ |Amt to Borrow = ___________ |Amt to Borrow = ___________ |

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|Loan C | | | |

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| |Down Payment = ___________ |Down Payment = ___________ |Down Payment = ___________ |

| |Amt to Borrow = ___________ |Amt to Borrow = ___________ |Amt to Borrow = ___________ |

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|Loan D | | | |

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| |Down Payment = ___________ |Down Payment = ___________ |Down Payment = ___________ |

| |Amt to Borrow = ___________ |Amt to Borrow = ___________ |Amt to Borrow = ___________ |

To calculate monthly payments, use the given formula:

where m = _______________________

A = _______________________

r = ________________________

n = ________________________

Appraise the different loans for the three houses you selected. SHOW YOUR SET-UP using the exponential function for each of the four loans on each house.

| |HOUSE 1 |HOUSE 2 |HOUSE 3 |

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|Loan A | | | |

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|Loan B | | | |

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|Loan C | | | |

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|Loan D | | | |

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TASK THREE: Selecting and defending your choice.

Now that you have calculated the monthly payment for each of the three desired choices, you must select a loan that would be best for you. After choosing the loan, explain how you made your selection. What are the positive aspects as well as the negative? Also, describe what would need to be in place with your life (i.e. job, education, partner, etc.) to attain the goal of owning this home.

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TASK FOUR: Growing wealth through healthy investments.

Imagine that you have been lucky enough to receive a $500 gift for the holidays. The only hitch is that you must research an investment strategy to see your money grow over time. Only after you do the math can you decide what you want with the gift, to invest it, or to spend it.

After researching different bank accounts to invest in, you have identified four that you are willing to consider. Each account will give you a different percentage rate and compounding occurrence .

• Bank of AmeriKa: 2.5% compounded biannually

• QuadCity Bank: 3.1% compounded annually

• I & M Bank: 0.95% compounded monthly

• Fells Wargo Bank: 1.6% compounded quarterly

You must choose which account you might deposit your gift into, given that you might want the money in 5 years, 10 years, or 30 years time.

• Compound Interest Formula:

• Identify the variables in the formula:

A = ____________________________ P = _________________________

r = _____________________________ n = _________________________

t = _____________________________

SHOW YOUR WORK FOR EACH!!!!

| |5 years |10 years |30 years |

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|Bank of AmeriKa | | | |

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|QuadCity Bank | | | |

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|I & M Bank | | | |

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|Fells Wargo Bank | | | |

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TASK FIVE: Selecting and defending your choice.

Based on your calculations above, you must write a letter to your benefactor to explain what you will do with the money. For instance, explain where you might choose to invest it. Explain how long you intend to keep your money in that account. Give justifiable reasons for your selected time period and bank so that your benefactor chooses to gift the money to you!

Benefactor’s Contact Information: Lynette Klipperstein

Director of Sales and Marketing

611 W. National Ave

Milwaukee, WI 53204

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