Available to invest = Portfolio = $

Available to invest = Portfolio = $1,000,000
Inflation rate = 2%

Step 1. Set up an "Amortization Table" to show exactly what's happening. We begin with $1 million. But we immediately make the first withdrawal, hence have less than $1 million to invest. We don't know how much we can withdraw initially, so we make a "guess" of $50,000. We subtract the $50,000 from the initial portfolio and get $950,000, which is invested at 5% and thus earns $47,500. The earnings are added to the beginning balance, less the withdrawal, to produce the ending balance, which is carried forward to create the next beginning balance. This process is continued for 15 years.

Step 2. We want to end up with a $0.00 ending balance. With the $50,000 initial withdrawal, we see that we end with more than zero. Therefore, we should make a larger initial withdrawal. We could just go through a series of trials and errors until we found an initial withdrawal that produced the zero ending balance. The amount that does the trick is $81,027.42. Replace the $50,000 with 81027.42 to prove that this value "works" to within one penny.

BOY
Beginning Amount Investable Ending
Balance Withdrawn Funds Earnings Balance
1 $1,000,000.00 $81,027.42 $918,972.58 $45,948.63 $964,921.21
2 $964,921.21 $82,647.97 $882,273.24 $44,113.66 $926,386.90
3 $926,386.90 $84,300.93 $842,085.97 $42,104.30 $884,190.27
4 $884,190.27 $85,986.95 $798,203.33 $39,910.17 $838,113.49
5 $838,113.49 $87,706.69 $750,406.81 $37,520.34 $787,927.15
6 $787,927.15 $89,460.82 $698,466.33 $34,923.32 $733,389.64
7 $733,389.64 $91,250.04 $642,139.61 $32,106.98 $674,246.59
8 $674,246.59 $93,075.04 $581,171.55 $29,058.58 $610,230.13
9 $610,230.13 $94,936.54 $515,293.59 $25,764.68 $541,058.27
10 $541,058.27 $96,835.27 $444,223.00 $22,211.15 $466,434.15
11 $466,434.15 $98,771.97 $367,662.18 $18,383.11 $386,045.29
12 $386,045.29 $100,747.41 $285,297.87 $14,264.89 $299,562.77
13 $299,562.77 $102,762.36 $196,800.41 $9,840.02 $206,640.43
14 $206,640.43 $104,817.61 $101,822.82 $5,091.14 $106,913.96
15 $106,913.96 $106,913.96 $0.00 $0.00 $0.00

Using Goal Seek:
1. Put the pointer on the cell for the Ending Balance after the 15th withdrawal.
2. Click Tools>Goal Seek to get a dialog box, which you then fill out as shown to the right.
3. You will be at the "Set cell" because you put the pointer there initially.
4. Go down to the "To value to" cell. You want to get 0 as the ending balance, so enter 0 here.
5. Now move down to the "By changing cell" box, then click on the cell with the Year 1 withdrawal and select it.
6. Now click OK, and the initial withdrawal will change to $81,027, and the final balance will go to $0.00. You could increase the decimals shown to see the extra digits Excel calculated.

Calculator solution:
Step 1: Find the real rate of return, rr.
rr = (1 + rNOM)/(1 + inflation) 1
rr = (1.05)/(1.02) 1
rr = 2.9412%

Step 2: Use the PMT function in Excel or a calculator to find the initial amount to be withdrawn. Be sure to set the calculator to BEGIN mode, and make a similar adjustment to the Excel function.
BEGIN
N = 15
I = rr = 2.9411765%
PV = 1,000,000
PMT = $81,027.42

This is consistent with the value found using Goal Seek.

165. Julian and Jonathan are twin brothers (and so were born on the same day). Today, both turned 25. Their grandfather began putting $2,500 per year into a trust fund for Julian on his 20th birthday, and he just made a 6th payment into the fund. The grandfather (or his estate's trustee) will make 40 more $2,500 payments until a 46th and final payment is made on Julian's 65th birthday. The grandfather set things up this way because he wants Julian to work, not be a "trust fund baby," but he also wants to ensure that Julian is provided for in his old age.

Until now, the grandfather has been disappointed with Jonathan and so has not given him anything. However, they recently reconciled, and the grandfather decided to make an equivalent provision for Jonathan. He will make the first payment to a trust for Jonathan today, and he has instructed his trustee to make 40 additional equal annual payments until Jonathan turns 65, when the 41st and final payment will be made. If both trusts earn an annual return of 8%, how much must the grandfather put into Jonathan's trust today and each subsequent year to enable him to have the same retirement nest egg as Julian after the last payment is made on their 65th birthday?
a. $3,726
b. $3,912
c. $4,107
d. $4,313
e. $4,528

ANS: A
Julian's retirement account Jonathan's retirement account
No. of payments thus far, Payment today 1
including today's payment 6
Number of remaining payments 40 40
N = total payments 46 N 41
I/YR 8.0% I/YR 8.0%
PV $0 PV $0
PMT $2,500 FV = Jonathan's FV = $1,046,065
FV Julian's FV = $1,046,065 PMT $3,726

Available to invest = Portfolio = $1,000,000
Inflation rate = 2%

Step 1. Set up an "Amortization Table" to show exactly what's happening. We begin with $1 million. But we immediately make the first withdrawal, hence have less than $1 million to invest. We don't know how much we can withdraw initially, so we make a "guess" of $50,000. We subtract the $50,000 from the initial portfolio and get $950,000, which is invested at 5% and thus earns $47,500. The earnings are added to the beginning balance, less the withdrawal, to produce the ending balance, which is carried forward to create the next beginning balance. This process is continued for 15 years.
 
Step 2. We want to end up with a $0.00 ending balance. With the $50,000 initial withdrawal, we see that we end with more than zero. Therefore, we should make a larger initial withdrawal. We could just go through a series of trials and errors until we found an initial withdrawal that produced the zero ending balance. The amount that does the trick is $81,027.42. Replace the $50,000 with 81027.42 to prove that this value "works" to within one penny.

BOY 
 Beginning Amount Investable Ending
 Balance Withdrawn Funds Earnings Balance
1 $1,000,000.00 $81,027.42 $918,972.58 $45,948.63 $964,921.21
2 $964,921.21 $82,647.97 $882,273.24 $44,113.66 $926,386.90
3 $926,386.90 $84,300.93 $842,085.97 $42,104.30 $884,190.27
4 $884,190.27 $85,986.95 $798,203.33 $39,910.17 $838,113.49
5 $838,113.49 $87,706.69 $750,406.81 $37,520.34 $787,927.15
6 $787,927.15 $89,460.82 $698,466.33 $34,923.32 $733,389.64
7 $733,389.64 $91,250.04 $642,139.61 $32,106.98 $674,246.59
8 $674,246.59 $93,075.04 $581,171.55 $29,058.58 $610,230.13
9 $610,230.13 $94,936.54 $515,293.59 $25,764.68 $541,058.27
10 $541,058.27 $96,835.27 $444,223.00 $22,211.15 $466,434.15
11 $466,434.15 $98,771.97 $367,662.18 $18,383.11 $386,045.29
12 $386,045.29 $100,747.41 $285,297.87 $14,264.89 $299,562.77
13 $299,562.77 $102,762.36 $196,800.41 $9,840.02 $206,640.43
14 $206,640.43 $104,817.61 $101,822.82 $5,091.14 $106,913.96
15 $106,913.96 $106,913.96 $0.00 $0.00 $0.00

Using Goal Seek:
1. Put the pointer on the cell for the Ending Balance after the 15th withdrawal.
2. Click Tools>Goal Seek to get a dialog box, which you then fill out as shown to the right.
3. You will be at the "Set cell" because you put the pointer there initially.
4. Go down to the "To value to" cell. You want to get 0 as the ending balance, so enter 0 here.
5. Now move down to the "By changing cell" box, then click on the cell with the Year 1 withdrawal and select it.
6. Now click OK, and the initial withdrawal will change to $81,027, and the final balance will go to $0.00. You could increase the decimals shown to see the extra digits Excel calculated.

Calculator solution:
Step 1: Find the real rate of return, rr.
 rr = (1 + rNOM)/(1 + inflation) 1
 rr = (1.05)/(1.02) 1
 rr = 2.9412%
 
Step 2: Use the PMT function in Excel or a calculator to find the initial amount to be withdrawn. Be sure to set the calculator to BEGIN mode, and make a similar adjustment to the Excel function.
 BEGIN
 N = 15 
 I = rr = 2.9411765% 
 PV = 1,000,000 
 PMT = $81,027.42 
 
 This is consistent with the value found using Goal Seek.

165. Julian and Jonathan are twin brothers (and so were born on the same day). Today, both turned 25. Their grandfather began putting $2,500 per year into a trust fund for Julian on his 20th birthday, and he just made a 6th payment into the fund. The grandfather (or his estate's trustee) will make 40 more $2,500 payments until a 46th and final payment is made on Julian's 65th birthday. The grandfather set things up this way because he wants Julian to work, not be a "trust fund baby," but he also wants to ensure that Julian is provided for in his old age.

Until now, the grandfather has been disappointed with Jonathan and so has not given him anything. However, they recently reconciled, and the grandfather decided to make an equivalent provision for Jonathan. He will make the first payment to a trust for Jonathan today, and he has instructed his trustee to make 40 additional equal annual payments until Jonathan turns 65, when the 41st and final payment will be made. If both trusts earn an annual return of 8%, how much must the grandfather put into Jonathan's trust today and each subsequent year to enable him to have the same retirement nest egg as Julian after the last payment is made on their 65th birthday?
a. $3,726
b. $3,912
c. $4,107
d. $4,313
e. $4,528

ANS: A
Julian's retirement account Jonathan's retirement account 
No. of payments thus far, Payment today 1
including today's payment 6 
Number of remaining payments 40 40
N = total payments 46 N 41
I/YR 8.0% I/YR 8.0%
PV $0 PV $0
PMT $2,500 FV = Jonathan's FV =  $1,046,065
FV Julian's FV = $1,046,065 PMT $3,726

0/5000

Từ: -

Sang: -

Kết quả (Việt) 1: [Sao chép]

Sao chép!

Available to invest = Portfolio = $1,000,000Inflation rate = 2%Step 1. Set up an "Amortization Table" to show exactly what's happening. We begin with $1 million. But we immediately make the first withdrawal, hence have less than $1 million to invest. We don't know how much we can withdraw initially, so we make a "guess" of $50,000. We subtract the $50,000 from the initial portfolio and get $950,000, which is invested at 5% and thus earns $47,500. The earnings are added to the beginning balance, less the withdrawal, to produce the ending balance, which is carried forward to create the next beginning balance. This process is continued for 15 years. Step 2. We want to end up with a $0.00 ending balance. With the $50,000 initial withdrawal, we see that we end with more than zero. Therefore, we should make a larger initial withdrawal. We could just go through a series of trials and errors until we found an initial withdrawal that produced the zero ending balance. The amount that does the trick is $81,027.42. Replace the $50,000 with 81027.42 to prove that this value "works" to within one penny. BOY Beginning Amount Investable Ending Balance Withdrawn Funds Earnings Balance1 $1,000,000.00 $81,027.42 $918,972.58 $45,948.63 $964,921.212 $964,921.21 $82,647.97 $882,273.24 $44,113.66 $926,386.903 $926,386.90 $84,300.93 $842,085.97 $42,104.30 $884,190.274 $884,190.27 $85,986.95 $798,203.33 $39,910.17 $838,113.495 $838,113.49 $87,706.69 $750,406.81 $37,520.34 $787,927.156 $787,927.15 $89,460.82 $698,466.33 $34,923.32 $733,389.647 $733,389.64 $91,250.04 $642,139.61 $32,106.98 $674,246.598 $674,246.59 $93,075.04 $581,171.55 $29,058.58 $610,230.139 $610,230.13 $94,936.54 $515,293.59 $25,764.68 $541,058.2710 $541,058.27 $96,835.27 $444,223.00 $22,211.15 $466,434.1511 $466,434.15 $98,771.97 $367,662.18 $18,383.11 $386,045.2912 $386,045.29 $100,747.41 $285,297.87 $14,264.89 $299,562.7713 $299,562.77 $102,762.36 $196,800.41 $9,840.02 $206,640.4314 $206,640.43 $104,817.61 $101,822.82 $5,091.14 $106,913.9615 $106,913.96 $106,913.96 $0.00 $0.00 $0.00Using Goal Seek:1. Put the pointer on the cell for the Ending Balance after the 15th withdrawal.2. Click Tools>Goal Seek to get a dialog box, which you then fill out as shown to the right.3. You will be at the "Set cell" because you put the pointer there initially.4. Go down to the "To value to" cell. You want to get 0 as the ending balance, so enter 0 here.5. Now move down to the "By changing cell" box, then click on the cell with the Year 1 withdrawal and select it.6. Now click OK, and the initial withdrawal will change to $81,027, and the final balance will go to $0.00. You could increase the decimals shown to see the extra digits Excel calculated.Calculator solution:Step 1: Find the real rate of return, rr. rr = (1 + rNOM)/(1 + inflation) 1 rr = (1.05)/(1.02) 1 rr = 2.9412% Step 2: Use the PMT function in Excel or a calculator to find the initial amount to be withdrawn. Be sure to set the calculator to BEGIN mode, and make a similar adjustment to the Excel function. BEGIN N = 15 I = rr = 2.9411765% PV = 1,000,000 PMT = $81,027.42 This is consistent with the value found using Goal Seek. 165. Julian and Jonathan are twin brothers (and so were born on the same day). Today, both turned 25. Their grandfather began putting $2,500 per year into a trust fund for Julian on his 20th birthday, and he just made a 6th payment into the fund. The grandfather (or his estate's trustee) will make 40 more $2,500 payments until a 46th and final payment is made on Julian's 65th birthday. The grandfather set things up this way because he wants Julian to work, not be a "trust fund baby," but he also wants to ensure that Julian is provided for in his old age.Until now, the grandfather has been disappointed with Jonathan and so has not given him anything. However, they recently reconciled, and the grandfather decided to make an equivalent provision for Jonathan. He will make the first payment to a trust for Jonathan today, and he has instructed his trustee to make 40 additional equal annual payments until Jonathan turns 65, when the 41st and final payment will be made. If both trusts earn an annual return of 8%, how much must the grandfather put into Jonathan's trust today and each subsequent year to enable him to have the same retirement nest egg as Julian after the last payment is made on their 65th birthday?a. $3,726
b. $3,912
c. $4,107
d. $4,313
e. $4,528

ANS: A
Julian's retirement account Jonathan's retirement account
No. of payments thus far, Payment today 1
including today's payment 6
Number of remaining payments 40 40
N = total payments 46 N 41
I/YR 8.0% I/YR 8.0%
PV $0 PV $0
PMT $2,500 FV = Jonathan's FV = $1,046,065
FV Julian's FV = $1,046,065 PMT $3,726

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Kết quả (Việt) 2:[Sao chép]

Sao chép!

Sẵn sàng đầu tư = Portfolio = $ 1.000.000
Tỷ lệ lạm phát = 2%

Bước 1. Thiết lập một "Khấu hao Bảng" để hiển thị chính xác những gì đang xảy ra. Chúng ta bắt đầu với $ 1 triệu. Nhưng chúng tôi ngay lập tức làm cho rút tiền đầu tiên, do đó có ít hơn $ 1 triệu để đầu tư. Chúng tôi không biết bao nhiêu chúng ta có thể rút ban đầu, vì vậy chúng tôi thực hiện một "đoán" là 50.000 $. Chúng tôi trừ đi 50.000 $ từ danh mục đầu tư ban đầu và nhận được 950.000 $, được đầu tư ở mức 5% và do đó kiếm được $ 47,500. Các khoản thu nhập được cộng vào số dư đầu năm, ít sự rút lui, để sản xuất số dư cuối kỳ, được chuyển sang tạo sự cân đối đầu tiếp theo. Quá trình này được tiếp tục trong 15 năm. Bước 2. Chúng tôi muốn kết thúc với một $ 0,00 dư cuối kỳ. Với sự rút lui ban đầu $ 50.000, chúng ta thấy rằng chúng ta kết thúc với nhiều hơn không. Do đó, chúng ta nên thực hiện rút tiền ban đầu lớn hơn. Chúng tôi chỉ có thể đi qua một loạt các thử nghiệm và sai sót cho đến khi chúng tôi tìm thấy một rút ban đầu sản xuất ra các số dư bằng không kết thúc. Số tiền hiện các trick là $ 81,027.42. Thay 50.000 $ với 81.027,42 để chứng minh rằng giá trị này "công trình" này với một đồng xu. BOY Bắt đầu Số tiền Investable Ending Balance Rút Quỹ Thu nhập Cân 1 $ 1,000,000.00 $ 81,027.42 $ 918,972.58 $ 45,948.63 $ 964,921.21 2 $ 964,921.21 $ 82,647.97 $ 882,273.24 $ 44,113.66 $ 926,386.90 3 $ 926,386.90 $ 84,300.93 $ 842,085.97 $ 42,104.30 $ 884,190.27 4 $ 884,190.27 $ 85,986.95 $ 798,203.33 $ 39,910.17 $ 838,113.49 5 $ 838,113.49 $ 87,706.69 $ 750,406.81 $ 37,520.34 $ 787,927.15 6 $ 787,927.15 $ 89,460.82 $ 698,466.33 $ 34,923.32 $ 733,389.64 7 $ 733,389.64 $ 91,250.04 $ 642,139.61 $ 32,106.98 $ 674,246.59 8 $ 674,246.59 $ 93,075.04 $ 581,171.55 $ 29,058.58 $ 610,230.13 9 $ 610,230.13 $ 94,936.54 $ 515,293.59 $ 25,764.68 $ 541,058.27 10 $ 541,058.27 $ 96,835.27 $ 444,223.00 $ 22,211.15 $ 466,434.15 11 $ 466,434.15 $ 98,771.97 $ 367,662.18 $ 18,383.11 $ 386,045.29 12 $ 386,045.29 $ 100,747.41 $ 285,297.87 $ 14,264.89 $ 299,562.77 $ 299,562.77 $ 13 $ 102,762.36 196,800.41 $ 9,840.02 $ 206,640.43 14 $ 206,640.43 $ 104,817.61 $ 101,822.82 $ 5,091.14 $ 106,913.96 15 $ 106,913.96 $ 106,913.96 $ 0,00 $ 0,00 $ 0,00 Sử dụng Goal Seek: 1. Đặt con trỏ vào ô cho dư cuối kỳ sau khi rút 15. 2. Nhấp vào Tools> Goal Seek để có được một hộp thoại, mà sau đó bạn điền vào như hình bên phải. 3. Bạn sẽ được ở "Thiết di động" bởi vì bạn đặt con trỏ có ban đầu. 4. Đi xuống "Để đánh giá để" tế bào. Bạn muốn nhận được 0 là số dư cuối kỳ, vì vậy nhập 0 ở đây. 5. Bây giờ di chuyển xuống "Bằng cách thay đổi tế bào" hộp, sau đó nhấp chuột vào các tế bào với việc thu hồi năm 1 và chọn nó. 6. Bây giờ bấm OK, và rút ban đầu sẽ thay đổi đến $ 81,027, và số dư cuối cùng sẽ đi đến $ 0,00. Bạn có thể làm tăng số thập phân hiển thị để nhìn thấy các chữ số phụ Excel tính toán. Giải pháp tính toán: Bước 1: Tìm tỷ lệ thực sự của lợi nhuận, rr. Rr = (1 + rNOM) / (1 + lạm phát) 1 rr = (1.05) /(1.02) 1 rr = 2,9412% Bước 2: Sử dụng chức năng PMT trong Excel hoặc một máy tính để tìm ra số tiền ban đầu được thu hồi. Hãy chắc chắn để thiết lập máy tính để BEGIN chế độ, và làm cho một sự điều chỉnh tương tự như chức năng của Excel. BEGIN N = 15 I = rr = 2,9411765% PV = 1,000,000 PMT = $ 81,027.42 Điều này phù hợp với các giá trị tìm thấy sử dụng Mục tiêu Seek. 165. Julian và Jonathan là anh em sinh đôi (và do đó được sinh ra trong cùng một ngày). Hôm nay, cả hai quay 25. Ông nội của họ bắt đầu đặt $ 2,500 mỗi năm vào một quỹ ủy thác cho Julian vào ngày sinh nhật thứ 20 của ông, và ông chỉ cần thực hiện thanh toán 6 vào quỹ. Các ông (hoặc người được ủy thác bất động của ông) sẽ làm cho hơn 40 $ 2500 thanh toán cho đến khi thanh toán lần thứ 46 và cuối cùng được thực hiện vào ngày sinh nhật lần thứ 65 của Julian. Các ông thiết lập những điều này vì ông muốn Julian để làm việc, không phải là một "tin tưởng quỹ bé", nhưng ông cũng muốn đảm bảo rằng Julian được quy định trong tuổi già của mình. Cho đến nay, ông đã thất vọng với Jonathan và nên đã không cho anh bất cứ điều gì. Tuy nhiên, mới đây họ đã hòa giải, và ông nội đã quyết định làm một điều khoản tương đương cho Jonathan. Ông sẽ thực hiện thanh toán đầu tiên một sự tin tưởng cho Jonathan ngày hôm nay, và ông đã chỉ đạo các ủy viên của mình để làm cho 40 thanh toán hàng năm bằng thêm cho đến khi Jonathan tròn 65, khi 41 và thanh toán cuối cùng sẽ được thực hiện. Nếu cả hai tin tưởng kiếm được một lợi nhuận hàng năm là 8%, có bao nhiêu phải ông nội đưa vào niềm tin của Jonathan ngày hôm nay và mỗi năm tiếp theo để cho phép anh ta để có cùng một trứng hưu tổ như Julian sau khi thanh toán cuối cùng được thực hiện vào ngày sinh nhật lần thứ 65 của họ? A. $ 3726 b. $ 3,912 c. 4107 $ d. 4313 $ e. $ 4528 ANS: Một của Julian tài khoản hưu trí của Jonathan hưu tài khoản số các khoản thanh toán cho đến nay, thanh toán ngày nay 1 kể cả hôm nay của thanh toán 6 Số tiền còn lại 40 40 N = tổng số tiền 46 N 41 I / YR 8,0% I / YR 8,0% PV 0 $ PV 0 $ PMT $ 2500 FV = Jonathan FV = $ 1.046.065 FV FV Julian = 1.046.065 $ PMT 3726 $

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Kết quả (Việt) 3:[Sao chép]

Sao chép!

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