Sequences & Series (id: f1e8e940e)

本题目来源于试卷: Sequences & Series，类别为 IB数学

[问答题]
Bill takes out a bank loan of 10000 x (ii2svsc.r60 dollars to buy a premium e*qe , zt28z3 xzs-qy/xndi0c alectric car, at an -z dqz,0x / a*zie 8n2qctxys3annual interest rate of 5.49 % . The interest is calculated at the end of each year and added to the amount outstanding.
1. Find the amount of money Bill would owe the bank after 10 years. Give your answer to the nearest dollar.

To pay off the loan, Bill makes quarterly deposits of P dollars at the end of every quarter in a savings account, paying a nominal annual interest rate of 3.2 % . He makes his first deposit at the end of the first quarter after taking out the loan.
2. Show that the total value of Bill's savings after 10 years is $P\left[\frac{{1.008}^{40}-1}{1.008-1}\right]$ .
3. Given that Bill's aim is to own the electric car after 10 years, find the value for P to the nearest dollar.

Melinda visits a different bank and makes a single deposit of Q dollars, the annual interest rate being 3.5 % .
4. 1. Melinda wishes to withdraw 8000 dollars at the end of each year for a period of n years. Show that an expression for the minimum value of Q is

$\frac{8000}{1.035}+\frac{8000}{{1.035}^2}+\frac{8000}{{1.035}^3}+\cdots +\frac{8000}{{1.035}^n}$ .

2. Hence, or otherwise, find the minimum value of Q that would permit Melinda to withdraw annual amounts of 8000 dollars indefinitely. Give your answer to the nearest dollar.

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