Continuous Interest

MAT 112

How Frequent?

How many periods?

Construct a new formula

A Little Math Trick

11

rtk

Pk

Call it “e”

Continuous Compound Interest

Note that here the exponent is “ rt ”, NOT “ mt ” as in the earlier formula.

12%, compounded continuously

Compare

Continuous Interest

CERTIFICATES OF DEPOSIT

Term Interest Rate% APY

3 Months up to 6 Months* 1.78 1.80

6 Months up to 1 Year* 2.08 2.10

1 Year up to 2 Years* 2.32 2.35

2 Years up to 4 Years* 2.96 3.00

4 Years up to 5 Years* 3.92 4.00

* $500.00 Minimum Opening Deposit

Interest is Compounded Continuously, credited monthly.

Penalty for early withdrawal.

http://www.hudsonriverbank.com/current_rates_sav.htm

Example

Another Example

Solving an equation

0.076000 3000 teIf not algebraically, then let’s try solving it graphically.

Finding the intersection0.076000 3000 te

Graph both sides of the equation and see where they’re equal.

Procedure for approximating the point of intersection.

Finding the intersection0.076000 3000 te

The balance reaches $6000 at around 9.9 years.

When compounded monthly…

120.08

16000 10000 112

t

For an account earning 8% compounded monthly, how long does it take for a deposit of $10000 to increase to a balance of $16000?

Graph it and solve.

When compounded monthly…

After 5.89 years (5 years, 11 months), the account has reached $16000.