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Investments: Where should you invest your money?
Learn how much to invest in different options.
You are a young entrepreneur and have started your own Internet website design
business. You have earned a profit that you would like to invest. Investing money can
make your money work for you by earning interest.
You have $7,000 to invest. You wish to earn a total annual interest of $476 which will
give you the extra money for a down payment on a car.
Your bank offered you the following investment options:


1 year certificate of deposit (CD) that pays 5% simple interest
A loan through ABC Mortgage Company that pays 8% simple interest for
1 year.
Question of the day: Based on this information, how much should you invest in the CD
and the loan?
Solution:
You will need to use the following formula when dealing with this type of money
problem:
i  prt
i = simple interest
p = principal (The principal is the amount of money you invest.)
r = interest rate (Remember to convert this percentage to a decimal before calculation!)
t = time measure in years
First, write down the “Givens” in the problem to help determine the values for the
variables in the formula i
 prt
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“Givens”:
$7,000 is the amount you have to invest. Therefore, p = $7,000
$476 is the TOTAL interest you want to earn from both investments. i = $476.
However, we have TWO investment options so we will need to set up a table to
determine “i” for each investment option. (Since there were two investments we can’t
simply plug values into i  prt .
Construct the following table to organize your information and help you solve this
problem. Place the givens for each account. (Note: The givens are in black.)
The goal of the problem is to find out how much you invest in each option. This means
we need to know the principal amount you invest in each option. Let “X” represent the
amount invested in the CD. The amount you invest in the loan would be the amount of
money left over after you invest in the CD. Therefore, the principal invested in the loan
would be 7,000 - X
The interest then needs to be calculated for the CD and Loan. Multiply across each row
to obtain this information.
Account Principal
Rate *
Time =
Interest
*
CD
X
5% = 0.05
1 year
X(0.05)(1) = 0.05X
Loan
7,000 - X
8% = 0.08
1 year
(7000 – X)(0.08)(1) =
560 – 0.08X
Next you must create an equation that involves the Total Interest. We know:
Interest from CD + Interest from Loan = Total Interest
The Total Interest you want to earn was given in the problem as $476.
Therefore, use the interest we found for the CD, Loan, and the given Total Interest.
0.05X  560  0.08X  476
Solve the equation for X to find the amount invested in the CD. You can then find the
amount invested in the Loan.
0.05X  560  0.08X  476
0.03X  560  476
0.03X  84
X  2800
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Note: 7000  x  7000  2800  4200 for the Loan.
Therefore, you need to invest $2,800 in the 5% CD and $4,200 in the 8% Loan to earn a
Total Interest of $476.
Another Example: Penelope has $12,000 and would like to invest her money. The two
investment options she is considering include:


A savings account that earns 8% simple interest.
A savings account that earns 7.25% simple interest.
How much should Penelope invest in each option if she wants to earn $900 in interest for
the year?
The following table and equation demonstrate how to set up and solve this problem.
Account
Principal
Rate *
Time =
Interest
X
8% = 0.08
1 year
X(0.08)(1) = 0.08X
12,000 - X
7.25% =
0.0725
1 year
(12,000 – X)(0.0725)(1) =
870 – 0.0725X
*
Savings
#1
Savings
#2
Equation:
0.08X  870  0.0725X  900
Solve the equation for X:
0.08X  870  0.0725X  900
0.0075X  870  900
0.0075X  30
X  4000
Therefore, Penelope should invest $4,000 at 8% and $8,000 at 7.25% to earn a Total
Interest of $900.
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INVESTMENT OPTIONS WORKSHEET
1.) Jack has earned a bonus of $20,000 at work. He invested this $20,000 into one
investment that pays 4% simple annual interest and another investment that pays 6%
simple annual interest. Jack earned $960 in interest after 1 year. How much did Jack
invest in each option? (Round to the nearest dollar.)
2.) Jane decided to invest a portion of her family inheritance. She invested $10,000 last
year. She invested in an option that paid 4.2% and an option that paid 5.75%. After one
year Jane earned $485.62. How much did Jane invest in each option? (Round to the
nearest dollar.)
Challenge Question:
3.) Ryan is going to invest $4,000 into two investment options. One option pays 3%
simple interest and the other option pays 3.5% percent simple interest. How much did
Ryan invest in each option if the interest earned in the option paying 3.5% simple interest
is $94.50 more than the interest earned in the 3% option?
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INVESTMENT OPTIONS WORKSHEET (ANSWER KEY)
1.) Jack has earned a bonus of $20,000 at work. He invested this $20,000 into one
investment that pays 4% simple annual interest and another investment that pays 6%
simple annual interest. Jack earned $960 in interest after 1 year. How much did Jack
invest in each option? (Round to the nearest dollar.)
Equation:
0.04 X 1200  0.06 X  960
X  12, 000
Therefore, Jack invested $12,000 at 4% and $8,000 at 6%.
2.) Jane decided to invest a portion of her family inheritance. She invested $10,000 last
year. She invested in an option that paid 4.2% and an option that paid 5.75%. After one
year Jane earned $485.62. How much did Jane invest in each option? (Round to the
nearest dollar.)
Equation:
0.042 X  575  0.0575X  485.62
X  5, 766
Therefore, Jane invested $5,766 at 4.2% and $4,234 @ 5.75%.
Challenge Question:
3.) Ryan is going to invest $4,000 into two investment options. One option pays 3%
simple interest and the other option pays 3.5% percent simple interest. How much did
Ryan invest in each option if the interest earned in the option paying 3.5% simple interest
is $94.50 more than the interest earned in the 3% option?
Equation:
0.03X  94.50  0.035(4000  X )
X  700
Therefore, Ryan should invest $700 at 3% and $3,300 at 3.5%.
Copyright 2007 Money Instructor