Transcript Combining Signed Numbers

Solving Investment Problems
Investment Problems
Investment problems have three parts:
1. The principal – the amount being invested
2. The rate – the % that the money will earn
3. The income – the earnings from the investment
The problem
Mary has just retired and has 60,000.00 available to invest.
She is considering bonds at an interest rate of 13%
and CD’s at an interest rate of 3%. If she wants to
earn income of exactly 6,000.00 per year from these
investments, how much money should she invest in
each?
Tic – tac - toe
Many problems are easiest to solve using boxes.
Principal
Bonds
CD
Total
Rate
Income
Fill the boxes with the information from the story.
bonds at an interest rate of 13% (write the % as a decimal)
Principal
Bonds
CD
Total
Rate
.13
Income
Fill the boxes with the information from the story.
CD at an interest rate of 3% (write the % as a decimal)
Principal
Rate
Bonds
CD
Total
.03
Income
Fill the boxes with the information from the story.
60,000.00 available to invest
Principal
Bonds
CD
Total
60,000
Rate
Income
Fill the boxes with the information from the story.
income of exactly 6,000.00
Principal
Rate
Income
Bonds
CD
Total
6,000
Tic – tac - toe
This is what we already know:
Principal
Rate
Bonds
.13
CD
.03
Total
60,000
Income
6,000
Tic – tac - toe
You don’t know how much was invested in bonds, so call that x.
Principal
Bonds
x
CD
Total
Rate
Income
.13
.03
60,000
6,000
Be smarter than the average bear!
You don’t know how much was invested in either bonds or
CD’s. You know the total is 60,000 and you have
called the amount invested in bonds x.
If you ever manage to figure out what x is, how will you
find the amount invested in CD’s?
You’ll take x away from the total of 60,000.
Let’s do it!
Tic – tac - toe
Show the amount in CD’s as the total minus x
Principal
Bonds
Rate
x
.13
CD
60,000 - x
.03
Total
60,000
Income
6,000
Tic – tac - toe
Multiply across: principal X rate = income
Principal
Rate
Income
x
.13
.13x
CD
60,000 - x
.03
.03 ( 60,000 – x )
Total
60,000
Bonds
6,000
Add down
You always add down because:
Income from bonds
+ Income from CD’s
_____________________
Total Income
Add down the last column
Principal
Rate
Income
x
.13
.13x
CD
60,000 - x
.03
.03(60,000 – x)
Total
60,000
Bonds
.13x + .03(60,000 - x) = 6,000
6,000
Solve the problem!
.13x + .03(60,000 - x) = 6,000
.13x + 1800 - .03x = 6000
.10x +1800 = 6000
.10x = 4200
x = 42,000
and 60,000 – x = 18,000
Be sure you answer the question!
how much money should she invest in each?
x = 42,000
and
60,000 – x = 18,000
She should invest 42,000 in bonds and 18,000 in CDs.
Tic-tac-toe Problems
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Make your boxes
Fill in the information you know
Use your head
Multiply across
Add down
Solve the problem
Make sure you answer the question
that is being asked!