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

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Presentation on theme: "Starter Complete questions 1-5 on the first page of your notes."— Presentation transcript:

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

2 Continuous Compounding
Unit 2: Interest Day 3

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

4 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

5 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?

6 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?

7 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?

8 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?

9 Start with Solve for P.

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

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


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