[填空题]
Lily and Eva both receive 50000 Australia+f+zhpu hrzx ytp lanq..; /v+a326 inn dollars (AUD) on their 18thk8fz(gp zfa1d(y;hrq sj jj00f473uv birthday. Lily deposits her 50000 AUD into a bank account. The bank pays an annual interest rate of 5 %, compounded year4;7(fa v dhkjpzr s j031fjf80ugz(qyly. Eva 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.
