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Tutorial 61:
Compound Interest: Future Value


WTAMU > Virtual Math Lab > College Algebra > Tutorial 61: Compound Interest: Future Value


 

checkAnswer/Discussion to 1a
$2000 for 12 months at an effective rate of 5%. 

 
ad1a

 
 
 
 
 

*Compound interest formula
 
 

*Plug in appropriate values
 

*Calculate inside (   )
 
 


 
The compound amount is $2100.

Taking the difference between the compound amount and the principle we get 2100 - 2100 = 100. 

Therefore, the compound interest is $100.

(return to problem 1a)


 


 

checkAnswer/Discussion to 2a
A $5000 certificate of deposit is purchased for $5000 and is held for six years.  If the certificate earns an effective rate of 5 1/4 % what is it worth at the end of that period? 

 
ad2a

 
 
 
 
 

*Compound interest formula
 
 

*Plug in appropriate values
 

*Calculate inside (   )
*Raise (  ) to the 6th power
 
 


 
The certificate deposit would be worth $6796.77

(return to problem 2a)


 


 

checkAnswer/Discussion to 3a
If an investor has a choice of investing money at 6% compounded daily or 6 1/8 % compounded quarterly, which is the better choice? 
 

Since we don’t have the amount on this problem, and there are two variables involved - rate and and number of compound period, we will have to find some common ground between the two choices.  We can’t assume that the larger of the two rates is going to give us a better outcome, because the compounding periods are different.  And we can’t assume that the more compounding periods is better because the rates are different.  So let’s change them both to effective rate - that will make the compounding period for both be annual or once a year, and then we can compare the rates. 

Let’s first change the 6% compounded daily to an effective rate:


 
ad3a

 
 
 

*Effective rate formula
 

*Plug in appropriate values
 

*Calculate inside (   )
*Raise (  ) to the 365th power
 
 
 


 
So the equivalent effective rate for 6% compounded daily would be 6.183%.
 

Next let’s change the 6 1/8% compounded quarterly to an effective rate:


 
ad3a2

 
 
 
 

*Effective rate formula

*Plug in appropriate values
 

*Calculate inside (   )
*Raise (  ) to the 4th power
 
 
 
 


 
So the equivalent effective rate for 6 1/8% compounded quarterly would be 6.267%.
 

Now we only have one variable - the rate.  Since they are both converted to an effective rate (compounded annually).  Comparing the two, it looks like 6 1/8% compounded quarterly would give a better return.  What do you think? 

(return to problem 3a)


 

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WTAMU > Virtual Math Lab > College Algebra > Tutorial 61: Compound Interest: Future Value


Last revised on October 6, 2011 by Kim Seward.
All contents copyright (C) 2002 - 2011 WTAMU and Kim Seward. All rights reserved.