Name ______________________________________________________ Date _______________________________
3-6 Continuous Compounding
Key Math Concepts
Continuous compound interest formula: B = pert
 r
Compound interest formula: B = P  1+ 
n
nt
Guided Exercises
8x − 3
, as the values of x increase towards infinity, use a
4x + 5
table to find out what happens to the values of h(x).
x
h(x)
1. Given the function h( x ) =
100 1.967901235
Find the value of h(x) for the values of x in the table.
h( x ) =
1,000 1.996754057
90,000 1.999963889
8x − 3
4x + 5
900,000
8,000,000
As the value of x increases, the value of the function
8x − 3
h( x ) =
approaches ____.
4x + 5
50,000,000
2. If you deposit $10,000 at 3.85% simple interest, what would your ending balance be
after three years?
Substitute.
I = prt = ________ × ________ × ________
The ending balance = ________ + ________ = ________
What would your ending balance be if the interest is compounded daily?
nt
 r

B = P  1+  = _______  1+
 n



Substitute.
(_____)(___)
≈ ____________
What would your ending balance be if the interest is compounded continuously?
B = pert = (__________)e(________)(____) ≈ ____________
Substitute.
The ending balance with simple interest is ____________.
The ending balance with interest compounded daily is ____________.
The ending balance with interest compounded continuously is ____________.
46
Financial Algebra Guided Practice Workbook 3-6
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied
or duplicated, or posted to a publicly accessible website, in whole or in part.
Name ______________________________________________________ Date _______________________________
Exercises
x
 1
3. Given the function f ( x ) =   , use a table to find lim f ( x ) .
x →∞
 2
4. Given the function f(x) = 2x, find lim f ( x ) .
x →∞
5. Eric deposits $4,700 at 5.03% interest, compounded continuously for five years. What
is his ending balance? How much interest did the account earn?
6. Find the interest for $50,000 for 2__12 years at a rate of 4.3% compounded monthly,
daily, hourly, and continuously.
7. Use a table of increasing values of x to find lim f ( x ) if f ( x ) =
x →∞
5x − 2
.
x +3
8. Find the interest earned on a $14,000 balance for nine months at 3__34 % interest
compounded continuously.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied
or duplicated, or posted to a publicly accessible website, in whole or in part.
Financial Algebra Guided Practice Workbook 3-6
47