Math 22 Natural Exponential Functions

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Limit Definition of

 The irrational number  is defined to be the limit:

Compound Interest

 Let  be the amount deposited,  the number of years,  the balance, 
 and  the annual interest rate (in decimal form).
 1. Compounded  times per year: 
 2. Compounded continuously: 

Exercises Find the balance in an account when $3000 is deposited for 10 years at an interest rate of 4%, compounded as follows.

a) Quarterly


a) Annually


a) Monthly


a) Daily


a) Continuously


Present Value

Exercises How much money should be deposited in an account paying 5% interest compounded monthly in order to have a balance of $20000 after 5 years?

This is present value problem. So

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