Fabulous Fund Raiser

Addy and Trey have received an anxious query from the president of the school.  Madison #1 Middle School has a proud tradition which involves 6th grade raising money that that will be used at the end of their 8th grade year for a community service project.  This year, the student’s 6th grade students held a bake sale which raised $500.  The school treasurer is concerned because the students want to build flower beds at the town’s senior center at a cost of $545.  Addy researches saving opportunities for the school and finds that:

First Nation Bank is offering a two-year CD with 4.9% simple interest.
Second National Bank is offering a two-year CD with 4.8% compound interest (compound yearly).

Hint:
Variables stand for:

I  =  interest accumulated
T = time
R = the actual interest rate

• I = P * R * T (Simple interest)
• Y = A (1 + R)^n (Compound interest)
• ~ Y= ending value, A = Starting Amount, R = Interest Rate, N = the number of time periods / The amount of interest can be determined by subtracting the starting principal amount from the ending principal amount.

Answer these questions:

1. Do they students need to hold another fund-raiser?  
2. How much will the class have in two years if it buys a First National Bank CD?
3. How much will the class have in two years if it buys a Second National Bank CD?
4. Which CD is the better deal?  Explain your thinking.  Did your calculations surprise you?

Bonus:
Assume next year’s 6th graders need $600 for its service project.  If it can buy a two-year CD with a compound interest rate of 5%, how much does it need to raise at its fund-raiser?

October 15th

Ummmmm!

2-for-1 Lunch

Trey and Andrew had just completed a particularly strenuous algebra class. They needed a break. Andrew was exhausted. "Boy, I'm glad to be out of there. I'll never use this stuff anyway." Trey agreed. "Yeah, let's go to Joe's Deli for lunch. I don't want to think about math for a while."

When Trey and Andrew arrived at Joe's Deli, Jake checked his wallet to make sure he had enough money for his meal. "Hey, we're in luck," he said excitedly. "I found a two-for-one coupon!"

"May I take your order?" asked the Joe's Deli waiter. Trey was pretty hungry. "I'd like a double cheeseburger with fries and a triple chocolate fudge sundae." That sounded good to Andrew. "Make that two," he added.  Trey was feeling pretty smug. "That two-for-one coupon makes this lunch even better. All of this and we're saving 50%."

"Yep, a no brainer," agreed Andrew. "We don't need math class to figure this one out."

Your challenge: Assume that the price of each meal is $P. The value of one of the meals is deducted from the total bill. A sales tax of 8 ¹/₄% will be paid on one of the meals, but the 15% tip will be paid on both meals.

Were the boys correct in their assertion that the percentage of savings is 50%? If yes, why? If not, what is the percentage of savings (rounded to the nearest whole percent)?

Please solve the problem in the general case as stated using $P, and not a specific number for P.

Bonus: Suppose the prices of two meals are $P and $A, with P > A. The two-for-one coupon states that you drop the meal of lower value. Assume the 8 ¹/₄% tax is paid on the more expensive meal, and the 15% tip is paid on both meals.

1. Find an expression for the percentage of savings in terms of A and P.
2. Use this expression to show that the maximum savings occur when A = P.

Oct 8th

At some point in your life you might have wondered … what if I could compete in a game show and earn some money fast …  Well here is your chance to practice.  Here is the situation:

Before you, you can see 10 closed doors.

The host tells you: ‘9 doors reveal nothing, one door hides a Ferrari…

If you choose the right one, it’s yours !’
You think and decide to take a door.
Just before opening that door, the host stops you…

The host opens eight doors to let you see there is nothing behind those doors.
Your door is still closed and he has left one other door closed too.






 






Now he asks: ‘Which door do you want to open ?
The one you already choose, or the one I am offering ?’
Which door do you choose ?

For the record:
- the game host does know where the ferrari is
- the game host has done the same with every contestant and will do the same every time (that is: opening eight empty doors, etc.).