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Worksheet: Exponential Growth: Compound Interest

Q1:

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 %

Q2:

Victoria has $ 1 0 0 0 0 that she wants to invest. Her bank has several investment accounts to choose from, all compounding daily. Her goal is to have $ 1 5 0 0 0 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.

Q3:

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 ) 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

Q4:

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.

Q5:

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

Q6:

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 %

Q7:

Anthony wants to buy an RV for his family holidays. He has researched the different models and decided he needs to spend about $ 2 8 0 0 0 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?

Anthony 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.

Q8:

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$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

Q9:

Jennifer decides to put $ 1 0 0 0 0 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 3 ) 𝑑
  • B 𝐴 = 1 0 0 0 0 β‹… ( 0 . 0 3 ) 𝑑
  • C 𝐴 = 1 0 0 0 0 β‹… ( 1 + 0 . 9 7 ) 𝑑
  • D 𝐴 = 1 0 0 0 0 β‹… ( 1 + 0 . 0 3 ) 𝑑
  • E 𝐴 = 1 0 0 0 0 β‹… ( 0 . 9 7 ) 𝑑

Q10:

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

Q11:

David invested $ 𝑉 in a fund with a guaranteed annual growth of 1 2 % .

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

  • A 1 . 1 2 ( 𝑉 ) 𝑑
  • B 𝑉 ( 0 . 8 8 ) 𝑑
  • C 0 . 8 8 ( 𝑉 ) 𝑑
  • D 𝑉 ( 1 . 1 2 ) 𝑑
  • E 𝑉 ( 0 . 1 2 ) 𝑑

The fund’s growth is calculated monthly.

We can rewrite the expression for the fund’s value as 𝑉 ο€½ 1 . 1 2  1 1 2 1 2 𝑑 .

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

Q12:

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.

Q13:

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 ) 3 𝑑
  • B 𝑀 ( 1 . 0 5 ) 𝑑 4
  • C 𝑀 ( 1 . 0 5 ) 𝑑 3
  • D 𝑀 ( 1 . 0 5 ) 4 𝑑
  • E 𝑀 ( 0 . 0 5 ) 4 𝑑

Q14:

Matthew invested $ 5 0 0 0 into an account with an interest rate of 4 . 5 % , compounded monthly. Write an equation to describe the amount, 𝐴 ( 𝑑 ) , in his account after 𝑑 years.

  • A 𝐴 ( 𝑑 ) = 5 0 0 0 ο€Ό 0 . 0 4 5 1 2  1 2 𝑑
  • B 𝐴 ( 𝑑 ) = 5 0 0 0 ο€Ό 1 + 0 . 4 5 1 2  𝑑
  • C 𝐴 ( 𝑑 ) = 5 0 0 0 ( 1 + 0 . 0 4 5 ) 1 2 𝑑
  • D 𝐴 ( 𝑑 ) = 5 0 0 0 ο€Ό 1 + 0 . 0 4 5 1 2  1 2 𝑑

Q15:

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 %