Mathematics AI HL
IB Questions
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Question 1 of 3
Marcus invested \(\$45000\) in a fixed deposit account with an annual interest rate of \(5.8\%\) compounded monthly.
Calculate the value of Marcus's investment after 3 years.
After \(m\) months, the amount of money in the fixed deposit account has appreciated to more than \(\$60000\).
Find the minimum value of \(m\), where \(m \in \mathbb{N}\).
Marcus is saving to purchase a new house. The price of the house is \(\$250000\).
Marcus makes an initial payment of \(30\%\) and takes out a loan to pay the rest.
Write down the amount of the loan.
Question 2 of 3
Sarah purchases a new car for \(\$35,000\). On the same day, her brother Tom buys a luxury vehicle for \(\$85,000\).
Sarah's car is expected to depreciate at a rate of 12% per year, while Tom's car will depreciate at a rate of 18% per year.
Calculate the value of Sarah's car after 4 years.
Find after how many years (\(k\)) both cars will have the same value.
Comment on the validity of your answer to part (b).
Question 3 of 3
Maya has \(\$750\) in her savings account. She considers investing the money for 4 years with a bank. The bank offers an annual interest rate of \(1.8\%\) compounded monthly.
Calculate the amount of money Maya would have at the end of 4 years with the bank. Give your answer correct to two decimal places.
Instead of investing the money, Maya decides to buy a laptop that costs \(\$750\). At the end of 4 years, the laptop will have a value of \(\$120\). It may be assumed that the depreciation rate per year is constant.
Calculate the annual depreciation rate of the laptop.