Simple Interest and Money Problems


Simple Interest and Money Problems

One type of money problem involves simple interest. The simple interest formula is:

interest = principal  ×  rate  ×  time

When working with interest problems involving two amounts, we often let the variable represent one amount of money, then represent the second amount in terms of the first. Other types of money problems may include finding costs for sales, unit prices, amounts of product, or adjustments in inventory.

Example

Jose has $15,000 to invest. He is considering two investments. One is a loan he can make to another party that pays him 8% simple interest for a year. A second investment is a 1-year certificate of deposit that pays 5%. Jose decides to place some money in each investment, and earns a total of $1,125 interest in 1 year from the two investments. How much money does he spend on each investment?

Understand
Let x = amount to be invested at 5%.
Then 15,000 − x = amount to be invested at 8%.
The sum of the investments is $1,125.

Use the simple interest formula to solve this problem.
interest = principal  ×  rate  ×  time


Translate
(interest from 5% CD) + (interest from 8% investment) = total interest
           0.05x             +        0.08(15,000 − x)           = 1,125

Solve
0.05x + 0.08(15,000 − x) = 1,125
0.05x + 0.08(15,000) − 0.08x = 1,125    distributive property
0.05x + 1200 − 0.08x = 1,125               multiply
-0.03x + 1200 = 1,125                        combine like terms
-0.03x = -75                                     subtract 1,200 from both sides
x = = 2,500                         divide both sides by -0.03

Answer

$2500 is invested at 5% interest.
15,000 − 2500 = $12,500 is invested at 8% interest.




Practice

1) Grassman's Appliance sells two kinds of microwaves, model one costs $130 and model two sells for $240. On a given day 10 microwaves were sold for a total of $1740. Determine the number of each model of microwave that were sold.

Let x = number of model one microwaves sold
Let 10 − x = number of model two microwaves sold

(income from model one) + (income from model two) = total income

 

 

 

 

2) James borrowed $5000 from a bank to help pay for a car. His loan was for 4 years at a simple interest rate of 8%. What is the total amount he will pay back to the bank including interest?

 

 

 

 

 

3) Kanisha put $6000 in a savings account earning 3% simple interest per year. When she withdrew her money, she received $840 in interest. How long had she left her money in the account?

 

 

 

 

 

4) Suppose Wal-Mart's stock is selling at $59 a share and Mattel's stock is selling at $28 a share. Beth has $6000 to invest. She wishes to purchase four times as many shares of the Wal-Mart stock as of Mattel. Only whole shares of stock can be purchased. How many shares of each will she purchase? How much money will be left over?

 

 

 

 

 

5) At a movie theater the evening show costs $7.50 and a matinee costs $4.75. On one day there was one matinee and one evening show of the same film. On that day a total of 310 adult tickets were sold, which resulted in ticket sales of $2022.50. How many adults went to the matinee and how many went to the evening show?















Answers

1.  6 of model one, 4 of model two

2.  $6600

3.  4

4.  88 shares of Wal-Mart, 22 shares of Mattel, $192 left over

5.  110 to the matinee, 200 to the evening show