Worksheet: Compound Interest

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

Q1:

James invests $3,000 at a 2% interest rate per year, compounded quarterly. Find the balance after 10 years.

  • A $ 4 , 4 6 6 . 5 9
  • B $ 3 , 6 6 2 . 3 8
  • C $ 5 , 4 3 4 . 0 8
  • D $ 3 , 3 1 3 . 8 7
  • E $ 3 , 6 5 6 . 9 8

Q2:

Amelia opened a retirement account with 7.25% APR in the year 2000. Her initial deposit was $13,500. 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 $ 5 4 , 7 1 4 . 2 9 , $299.19
  • B $ 3 3 , 3 2 1 . 8 3 , $182.21
  • C $ 3 2 , 2 2 3 . 3 0 , $176.20
  • D $ 8 2 , 2 4 7 . 7 8 , $449.75
  • E $ 2 2 , 7 0 0 . 2 5 , $124.13

Q3:

When Matthew was born, his grandparents invested $500 in a fund that would mature on his 21st birthday. If the fund earned 6% per year, compounded annually, how much was its value when it matured? Give your answer to the nearest dollar.

  • A $ 2 , 5 0 4
  • B $ 1 , 7 0 0
  • C $ 1 , 7 5 7
  • D $ 1 , 1 3 0
  • E $ 3 , 2 1 0

Q4:

An investment account with an annual interest rate of 7% was opened with an initial deposit of $4,000. Compare the values of the account after 9 years when the interest is compounded annually, quarterly, monthly, and continuously.

  • Aannually: $7,353.84, quarterly: $7,469.63, monthly: $7,496.71, continuously: $7,510.44
  • Bannually: $7,353.84, quarterly: $7,483.10, monthly: $7,492.16, continuously: $7,510.44
  • Cannually: $7,510.44, quarterly: $7,496.71, monthly: $7,469.63, continuously: $7,353.84
  • Dannually: $7,510.44, quarterly: $7,492.16, monthly: $7,483.10, continuously: $7,353.84
  • Eannually: $6,520, quarterly: $7,640, monthly: $9,880, continuously: $7,360

Q5:

Benjamin wants to save $54,000 for a down payment on a home. How much will he need to invest in an account with 8.2% APR, compounding daily, in order to reach his goal in 5 years?

Q6:

Charlotte deposits $1,500 into a retirement fund each year. The fund earns 8.2% 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 15% 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 $5,000 at a rate of 2.3% for 𝑑 years, compounded continuously?

  • A 𝑀 = 5 , 0 0 0 ο€Ό 1 + 0 . 0 2 3 1 2  
  • B 𝑀 = 5 , 0 0 0  οŽ–    
  • C 𝑀 = 5 , 0 0 0 𝑒  οŽ–    
  • D 𝑀 = 5 , 0 0 0 ( 1 + 0 . 0 2 3 𝑑 )

Q9:

Matthew decides to save $250 every month for 4 years. He can save in an account that pays annual interest of 3% or an account that pays annual interest of 2.5% compounded monthly. Which account will give the better return on his investment?

  • A the account that pays an annual interest of 3%
  • B the account that pays 2.5% compounded monthly

Q10:

A man deposited 1,569 LE in a bank account with an interest rate of 2% 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 9% 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 7% 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 7% 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 𝐴 offers depositors 4% annual interest compounded once per year. Bank 𝐡 offers 3.93% per year, compounded monthly.

Write an explicit formula for the return 𝑅 after 𝑛 years on a deposit of π‘…οŠ¦ dollars with both offers.

  • ABank A: 𝑅=𝑅(0.04), Bank B: 𝑅=𝑅1+0.039312
  • BBank A: 𝑅=𝑅(1+0.04), Bank B: 𝑅=𝑅1+0.039312
  • CBank A: 𝑅=𝑛𝑅(1+0.04), Bank B: 𝑅=12𝑛𝑅1+0.039312
  • DBank A: 𝑅=𝑅(1+0.04), Bank B: 𝑅=𝑅(1+0.0393)
  • EBank A: 𝑅=𝑅(1+0.04), Bank B: 𝑅=𝑅1+0.039312οˆοŠ¦ο‘ƒοŽ οŽ‘

Which bank’s 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 $2,000 to double if the interest rate is 3.5% 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 $3000 at an interest rate of 2% compounded continuously. After how many years and months will her investment be worth $3500?

  • 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 $10,000 that she wants to invest. Her bank has several investment accounts to choose from, all compounding daily. Her goal is to have $15,000 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 5%, compounded monthly. Write an equation he could use to work out 𝑉, the value of his investment in 3 years’ time.

  • A 𝑉 = 2 0 0 ( 5 ) 
  • B 𝑉 = 2 0 0 ο€Ό 5 1 2   
  • C 𝑉 = 2 0 0 ο€Ό 1 + 5 1 , 2 0 0  
  • D 𝑉 = 2 0 0 ο€Ό 1 βˆ’ 5 1 2   
  • E 𝑉 = 2 0 0 ο€Ό 1 + 5 1 , 2 0 0   

Q20:

A bank offers its customers an account with an interest rate of 3% compounded annually.

Write an equation that can be used to calculate 𝑆, the value of an investment that is left in the account for 𝑑 years. Let π‘†οŠ¦ represent the initial investment.

  • A 𝑆 = 𝑆 ( 0 . 9 7 )   
  • B 𝑆 = 𝑆 ( 0 . 9 7 )  
  • C 𝑆 = 𝑆 ( 1 . 0 3 )  
  • D 𝑆 = 2 𝑆 ( 1 . 0 3 )  
  • E 𝑆 = 𝑆 ( 0 . 0 3 )   

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 $1,500 in an account where interest was compounded continuously, how many years would have to pass to raise the value of the account to $4,500?

  • 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 6.03%, compounded quarter-yearly (once every 3 months).

Write the explicit formula for the return 𝑅 after 𝑛 years on a deposit of π‘…οŠ¦dollars.

  • A 𝑅 = 𝑅 ο€Ό 1 + 0 . 0 6 0 3 3    
  • B 𝑅 = 𝑅 ο€Ό 1 + 0 . 0 6 0 3 4   
  • C 𝑅 = 𝑅 ο€Ό 1 + 0 . 0 6 0 3 4   οŠͺ 
  • D 𝑅 = 𝑅 ο€Ό 0 . 0 6 0 3 4   οŠͺ 
  • E 𝑅 = 𝑅 ( 1 + 0 . 0 6 0 3 )  οŠͺ 

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

  • A 6 . 1 6 7 7 %
  • B 2 4 . 1 2 0 0 %
  • C 6 . 1 7 2 0 %
  • D 1 . 5 0 7 5 %
  • E 2 4 . 6 7 0 8 %

Q23:

Max wants to buy an RV for his family holidays. He has researched the different models and decided he needs to spend about $28000 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 4.5% 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 5.3%, 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 $10,000 in a savings account with an interest rate of 3% per year. What is the total amount of money 𝐴 that Jennifer will have in her savings account after 𝑑 years?

  • A 𝐴 = 1 0 , 0 0 0 β‹… ( 1 + 0 . 9 7 ) 
  • B 𝐴 = 1 0 , 0 0 0 β‹… ( 1 + 0 . 0 3 ) 
  • C 𝐴 = ( 1 + 0 . 0 3 ) 
  • D 𝐴 = 1 0 , 0 0 0 β‹… ( 0 . 0 3 ) 
  • E 𝐴 = 1 0 , 0 0 0 β‹… ( 0 . 9 7 ) 

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