Worksheet: Exponential Growth: Compound Interest

In this worksheet, we will practice solving questions on compound interest as a type of exponential growth.

Q1:

A bank offers a savings account with an annual interest rate. For an initial investment 𝐢 0 , the capital after 𝑑 years is given by 𝐢 = 𝐢 β‹… 1 . 0 2 5 0 𝑑 . What is the annual interest rate?

  • A 0 . 2 5 %
  • B 1 2 . 5 %
  • C 2 5 %
  • D 2 . 5 %
  • E 9 7 . 5 %

Q2:

During a boom in the real estate market, the value of properties increased on average by 1 5 % every year. What was the percentage increase every 5 years?

  • A 5 0 %
  • B 7 5 %
  • C 1 0 0 %
  • D 2 0 0 %
  • E 1 5 0 %

Q3:

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

  • A
  • B
  • C
  • D
  • E

Q4:

Shady 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?

Shady 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.

Q5:

An account pays 5 % interest every 3 months. On an initial deposit of 𝑀 d o l l a r s , what is the amount after 𝑑 years?

  • A 𝑀 ( 1 . 0 5 )  
  • B 𝑀 ( 1 . 0 5 )  
  • C 𝑀 ( 1 . 0 5 )  
  • D 𝑀 ( 1 . 0 5 ) οŠͺ 
  • E 𝑀 ( 0 . 0 5 ) οŠͺ 

Q6:

Karim invested in a fund with a guaranteed annual growth of .

Write an expression for the value of his fund after years.

  • A
  • B
  • C
  • D
  • E

The fund’s growth is calculated monthly.

We can rewrite the expression for the fund’s value as .

Use the new form of the expression to find the monthly growth rate. Give your answer to 3 significant figures.

Q7:

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

Q8:

Yara 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.

Q9:

Adam 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 ) 3
  • B 𝑉 = 2 0 0 ο€Ό 1 + 5 1 2 0 0  3
  • C 𝑉 = 2 0 0 ο€Ό 5 1 2  3 6
  • D 𝑉 = 2 0 0 ο€Ό 1 + 5 1 2 0 0  3 6
  • E 𝑉 = 2 0 0 ο€Ό 1 βˆ’ 5 1 2  3 6

Q10:

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 𝑆 0 represent the initial investment.

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

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.

Q11:

Sameh invested into an account with an interest rate of , compounded monthly. Write an equation to describe the amount, , in his account after years.

  • A
  • B
  • C
  • D

Q12:

If one put $ 1 5 0 0 in an account where interest was compounded continuously, how many years would have to pass to raise the value of the account to $ 4 5 0 0 ?

  • A 2 years
  • B 1 year
  • C 3 years
  • DIt cannot be determined from the information given.
  • E 4 years

Q13:

If you invest $ 5 0 0 0 in an account paying 4.5% interest compounded monthly, how much will the account be worth in 10 years?

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

Q14:

The return 𝑅 dollars after 𝑑 years on a savings account is given by the explicit formula 𝑅 = 1 2 3 4 ο€Ό 1 + 0 . 0 5 4  4 𝑑 . What are the meanings of the numbers 1 2 3 4 , 1.05, and 4?

  • AThe initial deposit is $ 1 2 3 4 ; the annual interest rate is 5 % and the number of deposit years is 4.
  • BThe initial deposit is $ 1 2 3 4 ; the annual interest rate is 1 . 2 5 % and it is compounded 4 times a year.
  • CThe initial deposit is $ 1 2 3 4 ; the annual interest rate is 1 . 2 5 % and the number of deposit years is 4.
  • DThe initial deposit is $ 1 2 3 4 ; the annual interest rate is 5 % and it is compounded 4 times a year.
  • EThe initial deposit is $ 1 2 3 4 ; the annual interest rate is 1 . 0 5 % and it is compounded 4 times a year.

Q15:

A savings account offers an annual interest rate of 6 . 0 3 % , compounded quarter-yearly (once every 3 months).

Write the explicit formula for the return 𝑅 after 𝑛 years on a deposit of 𝑅  d o l l a r s .

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

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

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