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IB Mathematics AI HL - Popular Quizzes

Compound Interest & Depreciation

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Question 1

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easy

[Maximum mark: 6]

Hannah buys a car for $24900\$24\hspace{0.15em}900. The value of the car depreciates by 1616 % each year.

  1. Find the value of the car after 1010 years. [3]

Patrick buys a car for $12000\$12\hspace{0.15em}000. The car depreciates by a fixed amount each year, and after 66 years it is worth $6200\$6200.

  1. Find the annual rate of depreciation of the car. [3]

easy

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Question 2

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easy

[Maximum mark: 6]

In this question give all answers correct to two decimal places.

Charlie deposits 80008000 Canadian dollars (CAD) into a bank account. The bank pays a nominal annual interest rate of 55 %, compounded semi-monthly.

  1. Find the amount of interest that Charlie will earn over the next 22 years. [3]

Oscar also deposits CAD into a bank account. His bank pays a nominal annual interest rate of 66 %, compounded quarterly. In 22 years, the total amount in Oscar's account will be $8000\$8000 CAD.

  1. Find the amount that Oscar deposits in the bank account. [3]

easy

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Question 3

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easy

[Maximum mark: 6]

Ali bought a car for $18000\$18\hspace{0.15em}000. The value of the car depreciates by 10.510.5 % each year.

  1. Find the value of the car at the end of the first year. [2]

  2. Find the value of the car after 44 years. [2]

  3. Calculate the number of years it will take for the car to be worth exactly half its original value. [2]

easy

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Question 4

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medium

[Maximum mark: 6]

Julia wants to buy a house that requires a deposit of 7400074\hspace{0.15em}000 Australian dollars (AUD).

Julia is going to invest an amount of AUD in an account that pays a nominal annual interest rate of 5.55.5 %, compounded monthly.

  1. Find the amount of AUD Julia needs to invest to reach 7400074\hspace{0.15em}000 AUD after 88 years. Give your answer correct to the nearest dollar. [3]

Julia's parents offer to add 50005000 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 3.53.5 %, compounded quarterly.

  1. Find the number of years it would take Julia to save the 7400074\hspace{0.15em}000 AUD if she accepts her parents money and follows their advice. Give your answer correct to the nearest year. [3]

medium

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Question 5

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medium

[Maximum mark: 12]

Lily and Eva both receive 5000050\hspace{0.15em}000 Australian dollars (AUD) on their 1818th birthday. Lily deposits her 5000050\hspace{0.15em}000 AUD into a bank account. The bank pays an annual interest rate of 55 %, compounded yearly. Eva invests her 5000050\hspace{0.15em}000 AUD into a high-yield mutual fund that returns a fixed amount of 30003000 AUD per year.

  1. Calculate:

    1. the amount in Lily's bank account at the end of the first year;

    2. the total amount of Eva's funds at the end of the first year. [2]

  2. Write down an expression for:

    1. the amount in Lily's bank account at the end of the nnth year;

    2. the total amount of Eva's funds at the end of the nnth year. [4]

  3. Calculate the year in which the amount in Lily's bank account becomes
    greater than the amount in Eva's fund. [2]

  4. Calculate:

    1. the interest amount that Lily earns if invested for 1212 years, giving your answer correct to two decimal places;

    2. the amount of funds that Eva earns for her investment if invested for 1212 years. [4]

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Question 6

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[Maximum mark: 14]

In this question, give all answers correct to the nearest whole number.

Ann is considering investing $85000\$85\hspace{0.15em}000 into a term deposit in one of two banks. The first bank offers an annual interest rate of 33 %, compounding monthly. The second bank offers a fixed payment amount of $250\$250 per month.

  1. Calculate:

    1. the amount that would be in the account in the first bank at the end of the first year;

    2. the amount that would be in the account in the second bank at the end of the first year. [4]

  2. Write down an expression for:

    1. the amount in the account in the first bank at the end of the nnth year;

    2. the amount in the account in the second bank at the end of the nnth year. [4]

  3. Calculate the year in which the amount in the first bank account becomes
    greater than the amount in the second bank. [2]

  4. Calculate:

    1. the interest that Ann would earn if she invested in the first bank for 1010 years;

    2. the interest that Ann would earn if she invested in the second bank for 1010 years. [4]

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