Compound Continuously

Multiple Choice

Caiden earned $475 from mowing lawns last summer. He deposited this money in an account that pays an interest rate of 3.8% compounded continuously. What will be his balance after 15 years?

• $141,962.02            

• $831.10                

• $839.93

• $846.80            

Multiple Choice

If $1,000 is invested at 16% interest, compounded continuously, for five years, what is the ending balance?

• $1,225,54
• $2,225.54
• $22,255.40
• $225.54

Multiple Choice

You invest $1600 at an annual interest rate of 4.6% compounded continuously. How much will you have in the account after 4 years.

• $1,923.23

• $10,138.07

• $6,701.28

• $800.26

Multiple Choice

Hugo opened a savings account and deposited $800 as principal. The account earns 4% interest, compounded continuously. What is the balance after 5 years?

• $832.00

• $977.12

• $973.32

• $960.00

Multiple Choice

Travis earned $180.72 doing odd jobs last summer and put it in a saving account that earns 15% interest compounded continuously. If he doesn't touch his money for 8 years, how much will he have?

• $400

• $500

• $553

• $600

What is Continuous Interest?

What is Continuous Interest?

Example:

Multiple Choice

Anthony deposits $1000 in an account that pays 1.25% interest compounded continuously. How much will be in his account after 3 years?

• $1014.67

• $1038.21

• $2,003.11

• $42521.08

Multiple Choice

Mr. T invested $15,000 in an account that pays 5% interest compounding continuously, how much is in the account after 5 years? 

• $15,500.50
• $19,260.38
• $19,260.40
• $21,500.25

Multiple Choice

If $7000 is invested at a continuously compounded interest rate of 6% for 5 years, what will be the total amount?

• The total amount will be $8000.

• The total amount will be $10000.

• The total amount will be $7000.

• The total amount will be $9313.94.

Multiple Choice

Mr. T invested $15,000 in an account that pays 5% interest compounding continuously, how much is in the account after 5 years? 

• $15,500.50
• $19,260.38
• $19,260.40
• $21,500.25

Multiple Choice

What does the P stand for in this formula?

• Initial amount

• Final amount

• Rate

• Time

• The number of times compounded per year.

Multiple Choice

Which formula is shown?

• Monthly compounded interest formula

• Annually compounded interest formula

• Continuously compounded interest formula

• Simple interest formula

Multiple Choice

What does the r stand for in this formula?

• Rate as a percent

• Rate as a decimal

• number of times interest is compounded

Multiple Choice

What does the t stand for in this formula?

• time in weeks

• time in months

• time in years

• the number of times interest is compounded per year

Multiple Choice

When would we use this formula? A = Pe ^rt

• interest increases by fixed amount
• compound interest 
• compound continuously 
• decreases by fixed percent

Fill in the Blanks

Dash invested $10,000 at 3% interest compounded continuously. How much will he have after 8 years?

Fill in the Blanks

Kimi invests $4,000 at 3% interest compounded continuously. How much money will she have in 4 years?

Fill in the Blanks

Damara invests $3500 at 2% compounded continuously for 5 years. How much will she have in her account after 5 years?

Multiple Choice

Willie invests $8,515 in a retirement account with a fixed annual interest rate of 5% compounded continuously. What will the account balance be after 20 years?

• $22,017.32

• $23,146.17

• $20,021.95

• $20,943.52

Multiple Choice

Jessica invests $3,948 in a savings account with a fixed annual interest rate of 9% compounded continuously. What will the account balance be after 11 years?

• $8,786.44

• $10,056.40

• $10,624.99

• $8,357.92

Multiple Choice

Adam invests $5,208 in a savings account with a fixed annual interest rate of 8% compounded continuously. What will the account balance be after 8 years?

• $9,876.87

• $10,699.49

• $9,489.59

• $8,803.91