# Worksheet: Compound Interest

In this worksheet, we will practice dealing with compound interest.

**Q2: **

Amelia opened a retirement account with APR in the year 2000. Her initial deposit was . How much will the account be worth in 2025 if the interest is compounded monthly? How much more would she make if the interest were compounded continuously?

- A , $299.19
- B , $182.21
- C , $176.20
- D , $449.75
- E , $124.13

**Q4: **

An investment account with an annual interest rate of was opened with an initial deposit of . Compare the values of the account after 9 years when the interest is compounded annually, quarterly, monthly, and continuously.

- Aannually: , quarterly: , monthly: , continuously:
- Bannually: , quarterly: , monthly: , continuously:
- Cannually: , quarterly: , monthly: , continuously:
- Dannually: , quarterly: , monthly: , continuously:
- Eannually: , quarterly: , monthly: , continuously:

**Q6: **

Charlotte deposits $1,500 into a retirement fund each year. The fund earns annual interest, compounded monthly. If she opened her account when she was 19 years old, how much will she have saved by the time she is 55? How much of that amount will be interest earned?

- A$4,008.23, $2,508.23
- B$4,008.23, $5,508.23
- C$28,429.43, $26,929.43
- D$28,429.43, $10,429.43
- E$28,000.43, $26,500.43

**Q7: **

Liam deposits $100 in a savings account that gives him a interest on his savings each month. Daniel has $350 in a cashing account that he withdraws $5 from each month. After how many months do the two have approximately the same bank balance?

**Q8: **

Which of the following functions describes the total amount of money available after investing at a rate of for years, compounded continuously?

- A
- B
- C
- D

**Q9: **

Matthew decides to save every month for 4 years. He can save in an account that pays annual interest of or an account that pays annual interest of compounded monthly. Which account will give the better return on his investment?

- A the account that pays an annual interest of
- B the account that pays compounded monthly

**Q10: **

A man deposited 1,569 LE in a bank account with an interest rate of per year. Determine how much money was in the account 5 years later, given that the interest was compounded quarterly. Give your answer correct to one decimal place.

**Q11: **

The price of an article increases by every year. Given that its original price was 3,652 LE, determine its price after 7 years. Give your answer to the nearest pound.

- A23,263 LE
- B27,865 LE
- C1,887 LE
- D6,676 LE

**Q12: **

A man deposited 1,078 LE in a bank account with an interest rate of per year. Determine how much money was in the account 5 years later, given that the interest was compounded monthly. Give your answer correct to one decimal place.

**Q13: **

A man deposited 5,094 LE in a bank account with an interest rate of per year. Determine how much money was in the account 19 years later, given that the interest was compounded annually. Give your answer correct to two decimal places.

**Q14: **

Bank offers depositors annual interest compounded once per year. Bank offers per year, compounded monthly.

Write an explicit formula for the return after years on a deposit of dollars with both offers.

- ABank A: , Bank B:
- BBank A: , Bank B:
- CBank A: , Bank B:
- DBank A: , Bank B:
- EBank A: , Bank B:

Which bankβs offer is better?

- ABank A
- BBank B
- CBoth offers are equivalent.

**Q15: **

To the nearest tenth of a year, how long will it take for an investment of to double if the interest rate is per year, compounded continuously?

**Q16: **

An investment compounded continuously tripled in five years. Find, to the nearest percent, the annual interest rate.

**Q17: **

Chloe invested at an interest rate of compounded continuously. After how many years and months will her investment be worth ?

- A7 years and 8 months
- B0 years and 8 months
- C7 years and 7 months
- D7 years and 10 months
- E7 years and 9 months

**Q18: **

Victoria has that she wants to invest. Her bank has several investment accounts to choose from, all compounding daily. Her goal is to have by the time she finishes graduate school in 6 years. Find, to the nearest hundredth of a percent, the minimum annual interest rate she would need. Solve the compound interest formula for the interest rate.

**Q19: **

Daniel invests $200 in an account that pays an annual interest rate of , compounded monthly. Write an equation he could use to work out , the value of his investment in 3 yearsβ time.

- A
- B
- C
- D
- E

**Q20: **

A bank offers its customers an account with an interest rate of compounded annually.

Write an equation that can be used to calculate , the value of an investment that is left in the account for years. Let represent the initial investment.

- A
- B
- C
- D
- E

If an amount of money is saved in the account, what will the percentage increase in its value be, provided it is left in the account for 5 years? Give your answer to the nearest percent.

**Q21: **

If one put in an account where interest was compounded continuously, how many years would have to pass to raise the value of the account to ?

- A1 year
- B4 years
- C2 years
- DIt cannot be determined from the information given.
- E3 years

**Q22: **

A savings account offers an annual interest rate of , compounded quarter-yearly (once every 3 months).

Write the explicit formula for the return after years on a deposit of .

- A
- B
- C
- D
- E

What annual percentage rate (compounded once a year) would give the same yield? Give your answer to 4 decimal places.

- A
- B
- C
- D
- E

**Q23: **

Max wants to buy an RV for his family holidays. He has researched the different models and decided he needs to spend about to get one suitable for his family. He wants to get a loan to pay for the RV and pay it off in 5 years. His bank charges annual interest, compounded monthly.

What is the monthly payment required to pay for the RV in 5 years?

Max can only afford to pay a maximum of $500 every month and does not want to make a down payment. What is the maximum he can pay for an RV? Give your answer to the nearest hundred dollars.

**Q24: **

Liam deposited $100 in an account with an annual interest rate of , where the amount of the interest is added to his account at the end of each year. Given that he did NOT withdraw any money in 3 years, determine the amount of money (in dollars and cents) in his account at the end of each year.

- A$105.30, $110.88, $116.76
- B$153.00, $161.11, $169.65
- C$153.00, $234.09, $358.16
- D$105.30, $110.60, $115.90
- E$110.88, $110.60, $116.76

**Q25: **

Jennifer decides to put in a savings account with an interest rate of per year. What is the total amount of money that Jennifer will have in her savings account after years?

- A
- B
- C
- D
- E