Compound Interest – College Algebra
I.
Simple Interest vs. Compound Interest:
***Please watch the following video and answer the questions:
http://goo.gl/UPp7rQ
Problem: Suppose you deposit $10,000 into the bank at an APR of 6%.
a. What does APR stand for?
b. How much do you have in the bank after 5 years with simple interest?
Interest Earned
Deposit
Amount in Bank
$10,000
End of Year 1
End of Year 2
End of Year 3
End of Year 4
End of Year 5
c. How much do you have in the bank after 5 years with compound
interest?
Interest Earned
Deposit
Amount in Bank
$10,000
End of Year 1
End of Year 2
End of Year 3
End of Year 4
End of Year 5
d. Describe the difference between simple and compound interest.
Compound Interest – College Algebra
II.
Compound Interest Formula:
𝒓 𝒏𝒕
𝑨 = (𝟏 + 𝒏)
***Please watch the following video: http://goo.gl/HdXJJE
a. Suppose you deposit $100 at an APR of 12% compounded quarterly.
How much do you have after 1 year? 2 years?
i. 1 year:
ii. 2 year:
III.
Continuously Compound Interest:
𝑨 = 𝑷𝒆𝒓𝒕
a. Suppose you deposit $100 at an APR of 12% compounded
continuously. How much do you have after 2 years?
Compound Interest – College Algebra
IV.
Practice Problems:
a. Suppose you deposit $5,000 into an account paying 6.5% interest
(APR). Find the amount in the account after 10 years if the money is
i. Compounded semiannually (2 times per year).
ii. Compounded quarterly (4 times per year).
iii. Compounded monthly.
iv. Compounded continuously.
b. Suppose you have $6,000 to invest. Which investment yields the
greater return over 4 years: 8.25% compounded quarterly or 8.3%
compounded semiannually?
c. Suppose you have $12,000 to invest. Which investment yields the
greater return over 3 years: 7% compounded monthly or 6.85%
compounded continuously?
Compound Interest – College Algebra
d. Mr. Krabs is able to borrow money from the Plankton at 11.9%
compounded daily (365 times per year). He neglects to do his
calculations and impulsively borrows $20,000 from Plankton and then
reinvests the money in the Bikini Bottom Bank at an APR of 12%
compounded every 6 months. Which picture below best describes the
way Mr. Krabs feels 5 years after he makes the deal?
Justify your answer with calculations and an explanation of your
choice.
e. Describe how Plankton feels about this deal? Is someone being
“ripped off”? Who? How are they being “ripped off”?