IB Mathematics AI HL - Popular Quizzes
Compound Interest & Depreciation
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Question 1
[Maximum mark: 6]
Hannah buys a car for . The value of the car depreciates by % each year.
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Find the value of the car after years. [3]
Patrick buys a car for . The car depreciates by a fixed amount each year, and after years it is worth .
- Find the annual rate of depreciation of the car.
[3]
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Question 2
[Maximum mark: 6]
In this question give all answers correct to two decimal places.
Charlie deposits Canadian dollars (CAD) into a bank account. The bank pays a nominal annual interest rate of %, compounded semi-monthly.
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Find the amount of interest that Charlie will earn over the next years. [3]
Oscar also deposits CAD into a bank account. His bank pays a nominal annual interest rate of %, compounded quarterly. In years, the total amount in Oscar's account will be CAD.
- Find the amount that Oscar deposits in the bank account.
[3]
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Question 3
[Maximum mark: 6]
Ali bought a car for . The value of the car depreciates by % each year.
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Find the value of the car at the end of the first year. [2]
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Find the value of the car after years. [2]
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Calculate the number of years it will take for the car to be worth exactly half its original value. [2]
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Question 4
[Maximum mark: 6]
Julia wants to buy a house that requires a deposit of Australian dollars (AUD).
Julia is going to invest an amount of AUD in an account that pays a nominal annual interest rate of %, compounded monthly.
-
Find the amount of AUD Julia needs to invest to reach AUD after years. Give your answer correct to the nearest dollar. [3]
Julia's parents offer to add AUD to her initial investment from part (a), however, only if she invests her money in a more reliable bank that pays a nominal annual interest rate only of %, compounded quarterly.
- Find the number of years it would take Julia to save the
AUD if she accepts her parents money and
follows their advice. Give your answer correct to the nearest
year. [3]
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Question 5
[Maximum mark: 12]
Lily and Eva both receive Australian dollars (AUD) on their th birthday. Lily deposits her AUD into a bank account. The bank pays an annual interest rate of %, compounded yearly. Eva invests her AUD into a high-yield mutual fund that returns a fixed amount of AUD per year.
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Calculate:
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the amount in Lily's bank account at the end of the first year;
-
the total amount of Eva's funds at the end of the first year. [2]
-
-
Write down an expression for:
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the amount in Lily's bank account at the end of the th year;
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the total amount of Eva's funds at the end of the th year. [4]
-
-
Calculate the year in which the amount in Lily's bank account becomes
greater than the amount in Eva's fund. [2]
-
Calculate:
-
the interest amount that Lily earns if invested for years, giving your answer correct to two decimal places;
-
the amount of funds that Eva earns for her investment if invested for years. [4]
-
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Question 6
[Maximum mark: 14]
In this question, give all answers correct to the nearest whole number.
Ann is considering investing into a term deposit in one of two banks. The first bank offers an annual interest rate of %, compounding monthly. The second bank offers a fixed payment amount of per month.
-
Calculate:
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the amount that would be in the account in the first bank at the end of the first year;
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the amount that would be in the account in the second bank at the end of the first year. [4]
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Write down an expression for:
-
the amount in the account in the first bank at the end of the th year;
-
the amount in the account in the second bank at the end of the th year. [4]
-
-
Calculate the year in which the amount in the first bank account becomes
greater than the amount in the second bank. [2]
-
Calculate:
-
the interest that Ann would earn if she invested in the first bank for years;
-
the interest that Ann would earn if she invested in the second bank for years. [4]
-
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