Paper 4D -Villanueva

8/11/2019 Paper 4D -Villanueva

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Patterns and Functions – Algebraic Thinking

K to 12 Competency: Number and Operations, Algebra, Problem Solving, Reasoning, Communications, Connecting, and RepresentationsMaterials Needed: Casio fx-300ES Calculato r, pencil and paper.

Steps for Solving the Problems

1. Press MODE . Enter 3 for Table.

2. At the f(x) = prompt, type in the compound interest formula.(For example, enter the expression 1,000(1+.05)X by pressing 1 0 0 0 ( 1 + .05)x _ ALPHA X.

3. Press = .

4. Where it says Start? , press 0 so that the equation will equal $1000at the beginning. Press = .D



5. When prompted to End? enter 10 to evaluate what the investment yields after10 years. Press =.

6. Enter 1 for the step because the investment is being compounded yearly.Press =.

7. Examine the table to determine what the $1,000 principal yields after each year.

8. Press AC to exit the table.



Name _______________________________________________Class ________________________Date ______________

Getting Started

Formula:

A = P • (1 + R)nt where A = the amount of money you willhave at a certain period of time

P = the starting amount of money you place into the account

R = the percentage of interest for the investment, n = the amount of timesyou will take the interest during the yeart = the number of years you hold onto that investment.

Use your calculator to solve each problem.

Problems

1. Given a $1,000 principal, how long will it take forthat money to double if you invest it at a rate of 5%compounded annually? ________________________

2. Given a $1,000 principal, how long will it take forthat money to double if you invest it at a rate of 8%compounded annually? ________________________

3. Given a $1,000 principal and a rate of 8%, how much money will thatinvestment be worth if you let in compound for:20 years? _______________ 40 years? _______________30 years? _______________ 50 years? _______________

4. What do you notice about the amount of your investment the longeryou let it compound?____________________________________________________________________________________________________________________________________________________________________________________________________________________________________

5. What happens to your investment over time if you increase the principal?____________________________________________________________________________________________________________________________________________________________________________________________________________________________________

6. What happens to your investment if your interest is compoundedsemi-annually, quarterly, or monthly instead of compounded annually?Use the table function to determine how the return changes when theprincipal is compounded semi-annually, quarterly, or monthly?____________________________________________________________________________________________________________________________________________________________________________________________________________________________________



Solutions:

1. The amount will double in the 15th year and will yield an amountof $2,078.90.

2. The amount will double in the 10th year and will yield an amountof $2,158.90.

3. for 20 years? [$4,660.90]

30 years? [$10,062.00]

40 years? [$21,724.00]

50 years? [$46,901.00]

4. The longer the time the investment is compounded, the moremoney you will have.

5. If you increase the amount of the principal, then you will have alarger return at the end of the investment.

6. There will be a greater return if you compound an investmentmonthly as opposed to quarterly, semi-annually, or annually.

Retrieved from:http://www.casioeducation.com/resource/pdfs/middle_school_and_the_fx300es.pdf

Submitted by: Angie VillanuevaM.A.Ed. Sec. Math

Paper 4D -Villanueva

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