2) Beginning three months from now, you want to be able to withdraw $3,500 each
ID: 2806919 • Letter: 2
Question
2) Beginning three months from now, you want to be able to withdraw $3,500 each quarter from your bank account to cover college expenses over the next five years. If the account pays 0.57 percent interest per quarter, how much do you need to have in your bank account today to meet your expense needs over the next five years?
3) You have 32 years left until retirement and want to retire with $3.3 million. Your salary is paid annually, and you will receive $46,000 at the end of the current year. Your salary will increase at 2.1 percent per year, and you can earn a 15.1 percent return on the money you invest. If you save a constant percentage of your salary, what percentage of your salary must you save each year? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
Explanation / Answer
Solution 2: Say you have X dollars in your account today. After three months you have to start paying $3500 each quarter for 5 years.
After 5 years total college expenses are $3500*4*5 = $70,000 ( 4 is multiplied as 3500 is to be paid each quarter so 4 quarters in a year)
So you need $70000 in your account by the end of 5 years to cover the expenses. So we will have to calculate the Present value of $70000 to get the money needed today in your account. Since bank is paying 0.57% interest on the money, X amount will grow by 1.0057 each quarter.however after 3 months yiu will start withdrawing $3500 from your account. So
1 quarter $X
2 quarter 1.0057X- 3500
3 quarter (1.0057X-3500)1.0057 - 3500
so on
21 Quarter (1.0057^20 X -3500(1.0057^19 +1.0057^18+......+1)
so, 70000 = (1.0057^20 X -3500(1.0057^19 +1.0057^18+......+1)
X= $124624 is the money you should have in your account today to meet the quarterly requirement of $3500.
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