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Worksheet: Compound Interest

Q1:

James invests $ 3 0 0 0 at a 2 % interest rate per year, compounded quarterly. Find the balance after 10 years.

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

Q2:

Amelia opened a retirement account with 7 . 2 5 % APR in the year 2000. Her initial deposit was $ 1 3 5 0 0 . 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 $ 5 0 0 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 $ 1 7 5 7
  • B $ 1 1 3 0
  • C $ 2 5 0 4
  • D $ 1 7 0 0
  • E $ 3 2 1 0

Q4:

Benjamin wants to save $ 5 4 0 0 0 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?

Q5:

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

Q6:

Matthew decides to save $ 2 5 0 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 2 . 5 % compounded monthly
  • B the account that pays an annual interest of 3 %

Q7:

To the nearest tenth of a year, how long will it take for an investment of $ 2 0 0 0 to double if the interest rate is 3 . 5 % per year, compounded continuously?

Q8:

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.

Q9:

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.

Q10:

Chloe invested $ 3 0 0 0 at an interest rate of 2 % compounded continuously. After how many years and months will her investment be worth $ 3 5 0 0 ?

  • A 0 years and 8 months
  • B 7 years and 7 months
  • C 7 years and 8 months
  • D 7 years and 9 months
  • E 7 years and 10 months

Q11:

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.

Q12:

An investment account with an annual interest rate of 7 % was opened with an initial deposit of $ 4 0 0 0 . Compare the values of the account after 9 years when the interest is compounded annually, quarterly, monthly, and continuously.

  • Aannually: $ 7 5 1 0 . 4 4 , quarterly: $ 7 4 9 6 . 7 1 , monthly: $ 7 4 6 9 . 6 3 , continuously: $ 7 3 5 3 . 8 4
  • Bannually: $ 7 3 5 3 . 8 4 , quarterly: $ 7 4 8 3 . 1 0 , monthly: $ 7 4 9 2 . 1 6 , continuously: $ 7 5 1 0 . 4 4
  • Cannually: $ 7 5 1 0 . 4 4 , quarterly: $ 7 4 9 2 . 1 6 , monthly: $ 7 4 8 3 . 1 0 , continuously: $ 7 3 5 3 . 8 4
  • Dannually: $ 7 3 5 3 . 8 4 , quarterly: $ 7 4 6 9 . 6 3 , monthly: $ 7 4 9 6 . 7 1 , continuously: $ 7 5 1 0 . 4 4
  • Eannually: $ 6 5 2 0 , quarterly: $ 7 6 4 0 , monthly: $ 9 8 8 0 , continuously: $ 7 3 6 0

Q13:

Liam deposits $100 in a savings account that gives him a 1 5 % 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?

Q14:

Bank 𝐴 offers depositors 4 % annual interest compounded once per year. Bank 𝐵 offers 3 . 9 3 % per year, compounded monthly.

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

  • ABank A: 𝑅 = 𝑅 ( 1 + 0 . 0 4 ) , Bank B: 𝑅 = 𝑅 ( 1 + 0 . 0 3 9 3 )
  • BBank A: 𝑅 = 𝑅 ( 0 . 0 4 ) , Bank B: 𝑅 = 𝑅 1 + 0 . 0 3 9 3 1 2
  • C Bank A: 𝑅 = 𝑛 𝑅 ( 1 + 0 . 0 4 ) , Bank B: 𝑅 = 1 2 𝑛 𝑅 1 + 0 . 0 3 9 3 1 2
  • DBank A: 𝑅 = 𝑅 ( 1 + 0 . 0 4 ) , Bank B: 𝑅 = 𝑅 1 + 0 . 0 3 9 3 1 2
  • EBank A: 𝑅 = 𝑅 ( 1 + 0 . 0 4 ) , Bank B: 𝑅 = 𝑅 1 + 0 . 0 3 9 3 1 2

Which bank’s offer is better?

  • ABank B
  • BBoth offers are equivalent.
  • CBank A

Q15:

Which of the following functions describes the total amount of money available after investing $ 5 0 0 0 at a rate of 2 . 3 % for 𝑡 years, compounded continuously?

  • A 𝑀 = 5 0 0 0 1 + 0 . 0 2 3 1 2
  • B 𝑀 = 5 0 0 0 ( 1 + 0 . 0 2 3 𝑡 )
  • C 𝑀 = 5 0 0 0
  • D 𝑀 = 5 0 0 0 𝑒

Q16:

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

Q17:

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.

  • A 1 887 LE
  • B 27 865 LE
  • C 23 263 LE
  • D 6 676 LE