3.1+Earning+Interest+0910

¹08 September 2009 O.C.J.P. ​ ​ __3.1 Earning Interest__ **BIG IDEA**: Many real world situations can be modelled and predicted using mathematics.


 * Essential question:** How can I model a non-linear relationship?

On the day Chantal was born, her Uncle Charlie used $100 to open a savings account. He planned to use the money in the account to buy Chantal a gift on her tenth birthday. Charlie forgot about the money until last week when he recieved an invitation to Chantal's fourteenth birthday party.

Charlie called Chantal and told her about the account. He said, "I'm sorry I forgot your tenth birthday. Would you like to give me the money that's in the account now, or would you like me to leave it in the bank and give it on your eighteenth birthday?"

The saving account that Charlie opened earns 8% interest each year. This means that at the end of each year, the bank calculates 8% of the baslance and adds this amount to the account. At the end of the first year, the interest earned was

I = 8% of $100 I = 0.08 * $100 I = $8

The interest was added to the account, giving a new balance of $108. So, on Chantal's first birthday there was $108 in the account.

At the end of the second year, the bank again calculated 8% interest and added it to the account. Since there was $108 in the account, the interest earned was

I = 8% of $108 I = 0.08 * $108 I = $8.64

This amount was added to the account, giving a new balance of $108+$8.64=$116.64. So on Chantal's second birthday there was $116.64 in the account.


 * Question:**


 * Charlie's account has been earning 8% interest at the end of every year since Chantal was born. Charlie has not deposited or withdrawn any money since he opened the account. How much money is in the account on Chantal's fourteenth birthday?**

The answer is $293.719 (3 d.p.)

This is how I got the answer:

After year 1:

$100+8% =($100*1.08)

After year 2:

($100*1.08)*1.08

After year 3:

($100*1.08)*1.08*1.08

And so after 14 years:

($100*1.08)*1.08¹³ =($100*1.08¹⁴)


 * __Follow-up:__**


 * 1) **Copy and complete the table to show the birthday year, the balance at the beginning of that year, and the interest earned at the end of that year. Your table should include data up through Chantal's fourteenth birthday.**


 * Birthday || Balance || Interest Earned ||
 * 0 (birth) || $100 || 8 ||
 * 1 || $108 || $8.64 ||
 * 2 || $116.64 || $9.33 ||
 * 3 || $125.97 || $10.07 ||
 * 4 || $136.04 || $10.88 ||
 * 5 || $146.93 || $11.75 ||
 * 6 || $158.68 || $12.69 ||
 * 7 || $171.38 || $13.71 ||
 * 8 || $185.09 || $14.80 ||
 * 9 || $199.90 || $15.99 ||
 * 10 || $215.89 || $17.27 ||
 * 11 || $233.16 || $18.65 ||
 * 12 || $251.81 || $20.14 ||
 * 13 || $271.96 || $21.75 ||
 * 14 || $293.71 || $23.49 ||

2. **Make a graph (birthday, balance) data from your table, and draw a straight line or curve to model the trend. Is the graph linear? Explain how you know.**




 * 3. About how much money will be in the account on Chantel's eighteenth birthday? Explain how you found your answer.**

There will be about $360.60 in the bank. I worked this out by (100*1.08¹⁸)

4. **Do you think Chantal should take the money now or wait for her eighteenth birthday? Explain you answer.**

I think she should wait because hten she'll have more money then than she would if she takes it out now.


 * 5. Is the pattern of change for these data similar to the pattern in the bridge-thickness data, the brige-length data or the teeter-totter data? Explain.**

It is similar to the bride-length data, as they were both inverse realtionships.