本题目来源于试卷: Sequences & Series，类别为 IB数学
[问答题]
Alex and Julie each t:uf*i/xrf2 qu /fly9 l7ngdufh+-(yhave a goal of sayo,e9q8 s3 3) msmxysiving 30000 dollars to put towards a house deposit. They each h)so38x y sm y3,9qsiemave 16000 dollars to invest.
1. Alex chooses his local bank and invests his 16000 dollars in a savings account that offers an interest rate of 5 % per annum compounded annually.
1. Find the value of Alex's investment after 7 years, to the nearest hundred dollars.
2. Alex reaches his goal after n years, where n is an integer. Determine the value of n .
2. Julie chooses a different bank and invests her 16000 dollars in a savings account that offers an interest rate of r % per annum compounded monthly, where r is set to two decimal places.
Find the minimum value of r needed for Julie to reach her goal after 10 years.
3. Xavier also wants to reach a savings goal of 30000 dollars. He doesn't trust his local bank so he decides to put his money into a safety deposit box where it does not earn any interest. His system is to add more money into the safety deposit box each year. Each year he will add one third of the amount he added in the previous year.
1. Show that Xavier will never reach his goal if his initial deposit into the safety deposit box is 16000 dollars.
2. Find the amount Xavier needs to initially deposit in order to reach his goal after 7 years. Give your answer to the nearest dollar.
参考答案: 
本题详细解析:
| 
