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Classwork: Compound Interest Date:_________________________________
Example 1: An amount of $1,500.00 is deposited in a bank paying an annual interest rate of 4.3%, compounded annually. What is the balance after 6 years?
Example 2: An amount of $1,500.00 is deposited in a bank paying an annual interest rate of 3.9%, compounded quarterly. What is the balance after 6 years?
Example 3: An amount of $1500 is deposited in a bank paying an annual interest rate of 4.2%, compounded monthly. What is the balance after 6 years?
Formula for Compound Interest:
Your Turn!
Which option gives you the best payout?
Option A) Invest $1800 at 5.65% interest compounded daily for 5 years.
Option B) Invest $1000 at 6% interest compounded semiannually for 20 years.
Let’s suppose 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, what will the value of the account be? What if it were compounded Semi-Annually? Quarterly? Monthly? Weekly? Daily? Hourly?
|Compounded |n= |Value, A |
|Annually | | |
|Semi-annually | | |
|Quarterly | | |
|Monthly | | |
|Weekly | | |
|Daily | | |
|Hourly | | |
|Every Minute | | |
|Every Second | | |
Describe the behavior of the sequence of numbers in the Value column.
Derivation of the Continuous Compound Interest Formula
|1. [pic] | |
|2. |Let [pic], so [pic] and [pic]. (Substitution) |
|3. [pic] | |
|4. [pic] | |
| | |
| | |
Application: Continuous Compounding
Example 4: Calculate the final amount for $1000 earning 7.6% interest compounding continuously for 8 years.
Your turn!
1. Suppose that $1000 is invested at 7% interest compounded continuously. How much money would be in the bank after 5 years?
2. Suppose that $1500 is invested at an interest rate of 8.5%. How much is the investment worth after 18 months if interest is compounded
a. quarterly?
b. continuously?
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