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IB MAI HL Number and Algebra Topic 1.3 Financial Mathematics (id: 2669177e0)

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admin 发表于 2024-2-6 01:33:10 | 显示全部楼层 |阅读模式
本题目来源于试卷: IB MAI HL Number and Algebra Topic 1.3 Financial Mathematics,类别为 IB数学

[填空题]
Lily and Eva both receive 50000 Australian dolgd (,0ub a,qjnlars (AUD) on their 18th bi(jdw5a, 9 v0tt v4tedlrthday. Lily deposits her 50000 AUD into a bank account. The bank pays an annual interest rate of 5 %, compounded yearly. E, tdevtv(l9j4dt0 a 5wva invests her 50000 AUD into a high-yield mutual fund that returns a fixed amount of 3000 AUD per year.

1.Calculate:

1.1.the amount in Lily's bank account at the end of the first year;
Hence, using the compound interest formula, we get FV=  AUD.
1.2.the total amount of Eva's funds at the end of the first year.
We have FV=  .
2.Write down an expression for:

2.1.the amount in Lily's bank account at the end of the nth year;
Hence, using the compound interest formula, we obtain FV=x(1+y)$^n$.x=  ,y=  .
2.2.the total amount of Eva's funds at the end of the nth year.
We have FV=50000+(x)n.x=  .
3.Calculate the year in which the amount in Lily's bank account becomes
greater than the amount in Eva's fund.
Hence this will happen in   th year

4.Calculate:

4.1.the interest amount that Lily earns if invested for 12 years, giving your answer correct to two decimal places;

4.2.the amount of funds that Eva earns for her investment if invested for
12 years.




参考答案:
空格1: 52500空格2: 53000空格3: 50000空格4: 0.05空格5: 3000空格6: 9


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