Discovery of E Name:

Compound – interest paid on the principal of an investment and any previously earned interest.

A -> P-> r-> n-> t->

1) An investment account pays 4.2% annual interest compounded monthly. If $2500 is invested in this account, what will be the balance after 15 years?

Set up the equation:

A =

2) Find the balance of an account after 7 years if $700 is deposited into an account paying 4.3% interest compounded monthly.

John Bernoulli discovered something by studying a question about . (Who is John Bernoulli? Johann Bernoulli (27 July 1667 – 1 January 1748) was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is known for his contributions to infinitesimal calculus and educated in his youth. (Source: Wikipedia)

Ready to be John Bernoulli? An account starts with $1.00 and pays 100 percent interest per year. If the interest is credited once, at the end of the year, the value of the account at year-end will be $2.00. What happens if the interest is computed and credited more frequently during the year?

Write your prediction here: ______

______

Let’s do solve this mathematically using compound formula.

Frequency (number of compounding Equation Total periods each year.)

Once a year $2.00

Twice a year $2.25

Yay! We made $0.25 more! Compound bimonthly

Compound monthly

Compound weekly

Compound daily

Compound hourly

Compound secondly

What did you observe from the above table? Can we ever reach $3? ______

______

Bernoulli noticed that this sequence approaches a limit with larger n and, thus, smaller compounding intervals. Compounding weekly (n = 52) yields $2.692597..., while compounding daily (n = 365) yields $2.714567..., just two cents more. The limit as n grows large is the number that came to be known as e; with continuous compounding, the account value will reach $2.7182818....

You have just discovered e!

1) What kind of number is e?

2) Why is “e” an important number in math?

3) What does “LN” represent?