Starter Complete questions 1-5 on the first page of your notes.

Continuous Compounding Unit 2: Interest Day 3

Compounding Continuously You describe a function that compounds interest as frequently as possible as a function that compounds interest continuously.

Formula for Compounding Continuously A= Pe rt A = accumulated balance e is not a variable!!!!!!!!!! r = interest rate as a decimal t = time in years

Example 1 Suppose $5000 is put into an account that pays 4% compounded continuously. How much will be in the account after 3 years? Is this amount smaller or larger than compounding daily? If so, by how much?

Example 2 If $8000 is invested in an account that pays 4% interest compounded continuously, how much is in the account at the end of 10 years?

Example 3 If interest is compounded continuously at 4.5% for 7 years, how much will a $2000 investment be worth at the end of 7 years?

Planning Ahead Suppose you want to have $100,000 for your baby to go to college in 18 years. How much would you have to deposit today into an account that is compounded continuously?

Start with Solve for P.

Example 4: Use the info above and an account that accrues an APR of 3.5%. Find how much you need to deposit today.

Example 5: How much would you have to deposit today to have $450,000 in 40 years? Your investment will accrue 5% compounded continuously.