Continuous Compounding

1. A bank representative studies compound interest, so she can better serve customers.

She analyzes what happens when $2,000 earns interest several different ways at a rate of 4% for 3

years.

a. Find the interest if it is computed using simple interest.

b. Find the interest if it is compounded annually.

c. Find the interest if it is compounded semiannually.

d. Find the interest if it is compounded quarterly.

e. Find the interest if it is compounded monthly

f. Find the interest if it is compounded daily.

g. Find the interest if it is compounded hourly.

h. Find the interest if it is compounded every minute.

i. Find the interest if it is compounded continuously.

j. What is the difference in interest between simple interest an interest compounded

continuously?

2. Find the interest earned on a $50,000 deposited for six years at 4 1/8% interest, compounded

continuously.

3. Whitney deposits $9,000 for two years. She compares two different banks. State Banks will pay

her 4.1% interest, compounded monthly. Kings Savings will pay her 4.01% interest, compounded continuously.

a. How much interest does State Bank Pay?

b. How much interest does Kings Savings Pay?

c. Which bank pays higher interest? How much higher?

d. What other factors might affect Whitney's choice besides inter

est?

4. Find the interest earned on a $30,000 deposit for six months at 4 % interest, compounded

continuously.

5. Samuel wants to deposit $4,000 and keep that money in the bank without deposits or

withdrawals for three years. He compares two different options.

Option 1 will pay 3.8% interest, compounded quarterly.

Option 2 will pay 3.5 % interest, compounded continuously.

a. How much does Option 1 pay?

b. How much does Option 2 pay?