PreCalculus
Interest Word Problems
Name________________________
Date_________________
Congratulations!! You have just won $50,000! You decide to invest your money and the
bank presents you with two investment options. You may either invest your $50,000 at 5%
interest, compounded monthly, for a period of ten years OR you can invest that $50,000 at
5% interest, compounded continuously, for ten years. You must figure out which investment
option will yield a greater profit.
You have already learned how to use the rules of exponents to solve math problems and to solve
exponential equations. Now you will apply these concepts to solve interest problems.
There are several types of interest problems. This lesson deals with solving problems where
interest is compounded and where interest is continuous.
x
x
To “compound” interest means adding the accumulated interest back to the original amount
in the account.
To “continuously compound” interest means adding interest every instant
The Compound Interest Formula is A
§
P ¨1 ©
r·
¸
n¹
nt
A represents
P represents
r represents
t represents
n represents
Let’s try some examples using the Compound Interest Formula…
1. Suppose Wes has $1000 that he invests in an account that pays 3.5% interest compounded
quarterly. How much money does Wes have at the end of 5 years? How much interest will
he earn?
PreCalculus
Interest Word Problems
A
§ r·
P ¨1 ¸
© n¹
Name________________________
Date_________________
nt
2. William wants to have a total of $4000 in two years so that he can put a hot tub on his deck.
He finds an account that pays 5% interest compounded monthly. How much should William
put into this account so that he’ll have $4000 at the end of two years?
3. Suppose William, from our last example, only has $3500 to invest but still wants $4000 for
a hot tub. He finds a bank offering 5.25% interest compounded quarterly. How long will he
have to leave his money in the account to have $4000?
PreCalculus
Interest Word Problems
Name________________________
Date_________________
Interest that is compounded continuously seldom occurs at banks that you might deal with on a
regular basis. However it is very useful for finding the maximum amount of money that can be
earned at a particular interest rate. It is a very effective way to demonstrate how powerful
compounding interest can be.
You should be careful to note that for interest compounded for any amount of time other than
continuously, there is a different formula (the one you learned to use in the previous examples).
The following applies only to interest compounded continuously.
The formula for continuously compounded interest is A
Pe rt
A, P, r and t represent the same quantities described in the compound interest problems above. The
letter e is not a variable. It has a numeric value (approximately ____________) although we do not
usually use the value. We simply solve the problem using the “e” button on the calculator.
Let’s try some examples using the formula for Continuously Compounded Interest…
4. Suppose $5000 is put into an account that pays 4% compounded continuously. How much
will be in the account after 3 years?
5. If interest is compounded continuously at 4.5% for 7 years, how much will a $2000
investment be worth at the end of 7 years?
6. How long will it take $3000 to double if it is invested in an account that pays 3%
compounded continuously?
PreCalculus
Interest Word Problems
Name________________________
Date_________________
Now let’s go back and figure out which is the best investment option for our lottery winnings. I
have re-typed the problem for you. I will collect this problem at the start of class tomorrow and
grade it out of 10 points (this will be your first grade of the 4th quarter!). Your score will be based
on the accuracy of your mathematical calculations as well as the amount of work that you show, so
use the examples we did in class to help you out. Good luck!
Congratulations!! You have just won $50,000! You decide to invest your money and the
bank presents you with two investment options. You may either invest your $50,000 at 5%
interest, compounded monthly, for a period of ten years OR you can invest that $50,000 at
5% interest, compounded continuously, for ten years. Which investment option will yield a
greater profit?
PreCalculus
Interest Word Problems
Name________________________
Date_________________
Homework:
Read each problem carefully and decide which interest formula you need to solve. Show all work!
A
§ r·
P ¨1 ¸
© n¹
nt
A
Pert
1. Mildred plans to put her graduation money into an account and leave it there for 4 years
while she goes to college. She receives $750 in graduation money that she puts it into an
account that earns 4.25% interest compounded semi-annually. How much will be in
Mildred’s account at the end of four years?
2. ABC Bank is offering to double your money! They say that if you invest with them at 6%
interest compounded quarterly they will double your money. If you invest $1500 in the
account, how long will it take to double your money?
3. If $8000 is invested in an account that pays 4% interest compounded continuously, how
much is in the account at the end of 10 years?
PreCalculus
Interest Word Problems
Name________________________
Date_________________
nt
§ r·
P ¨1 ¸
A Pert
© n¹
4. How long will it take $4000 to triple if it is invested at 5% compounded continuously?
A
5. Lindsay wants to have a total of $3500 in two years so she can take a trip to St. Maarten.
She finds an account that pays 4% interest compounded monthly. How much should
Lindsay put into this account so that she’ll have $3500 at the end of two years?
6. Miss Young wants to have a total of $30,000 in three years so that she can buy a house. She
finds an account that pays 4.25% interest compounded monthly. How much should Miss
Young put into this account so that she’ll have $30,000 at the end of three years?
7. Miss Young wants to have a total of $10,000 in two years so that she can travel around the
world. Suppose she finds an account that pays 3.25% interest compounded continuously.
How much should Miss Young put into this account so that she’ll have $10,000 at the end
of two years?