8.2 Day 2

Compound Interest if compounding occurs in different intervals.

A = P ( 1 + r/n)nt

Examples of Intervals: Annually, Bi-Annually, Quarterly, Monthly, Weekly, Daily…….)

Ex 1: Find the final amount of a $100 investment after 10 year at 5% interest, compounded annually, quarterly, monthly and daily.

What happens when we use the formula and n continues to get larger???Lets use the formula y = (1 +1/n)n to see.

The number e.

The number e is an irrational number approximately equal to 2.71828.

Exponential functions with the base e are useful for describing continuous growth or decay.

Continuously Compounded Interest Formula

A = Pert

Ex 2: You invest $1050 in an account that pays 5.5% interest compounded continuously. How much money will you have in the account after 5 years?

Ex 3: A college graduate wants to save $10,000 for a new car in 3 years. How much should he put in an account that earns 4.5% interest compounded continuously?