Question

Problem 4-62 (algorithmic) Question Help A person deposits $3,000 in an account each year for five years (starting at the end of year one). At the end of the fifth year, one-half of the account balance is withdrawn: $6,000 is deposited annually for five more years (starting in the 6th year), with the total balance withdrawn at the end of the fifteenth year. There are no additional payments in years 11-15. a. Choose the correct cash flow diagram. b. If the account earns interest at the rate of 7% per year, how much is withdrawn at the end of five years? C. If the account continues to earn interest at the rate of 7% per year, how much is withdrawn at the end of 15 years? Click the icon to view the interest and annuity table for discrete compounding when i = 7% per year. a. Choose the correct cash flow diagram below. ОА. F15 O O F15 18 10 11 12 13 14 15 7_345 67 8 9 10 11 12 13 14 15 ЗК ЭКЗК ЭКЗК ак ак как акт BK BK BK BK BK Вк вк ак вк Вк O c. OD ок ок ок ок ок | ак ак ак к ок O O O F5/5 OOO 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 F5/2 3к 3к 3к ак ЗК І 1 1 1 1 1 Вк Вк ак вк Вк

Answer 1

a) From an investor perspective, amount invested is cash out which is represented by downward arrow in cash flow while money withdrawed is cash in which is represented by upward arrow. It is clearly depicted in option B.

Option A starts investing money from 2nd year which makes this option incorrect.

Option C shows inverse arrows of cash in and cash out which makes this option incorrect.

Option D withdraw one fifth of the money after year 5 while actually half of the money was withdrawn. Thus this option is also incorrect.

b) Investment of $3,000 from year 1 to year 5.

Money invested in first year will be saved for 4 years as they were invested at end of year 1 till end of year 5. It will become 3,000 (1 + 0.07)4 = 3,932.38 at the end of 5th year.

Money invested in second year will be saved for 3 years as they were invested at end of year 2 till end of year 5. It will become 3,000 (1 + 0.07)3 = 3,675.12 at the end of 5th year.

Money invested in third year will be saved for 2 years as they were invested at end of year 3 till end of year 5. It will become 3,000 (1 + 0.07)2 = 3,434,7 at the end of 5th year.

Money invested in forth year will be saved for 1 years as they were invested at end of year 4 till end of year 5. It will become 3,000 (1 + 0.07)1 = 3,210 at the end of 5th year.

Money invested in fifth year will be saved for 0 years as they were invested at end of year 5 till end of year 5. It will become 3,000 (1 + 0.07)0 = 3,000 at the end of 5th year.

Value of total money at the end of 5th year = 3,932.38 + 3,675.12 + 3,434.7 + 3,210 + 3,000 = 17,252.2

Half of it is withdrawed which is 8,626.1 while half of the money will be invested till end of year 15.

c) Rate of interest = 7% compounded annually

Investment of $6,000 from year 6 to year 10.

Money invested in sixth year will be saved for 9 years as they were invested at end of year 6 till end of year 15. It will become 6,000 (1 + 0.07)9 = 11,030.75 at the end of 15th year.

Money invested in seventh year will be saved for 8 years as they were invested at end of year 7 till end of year 15. It will become 6,000 (1 + 0.07)8 = 10,309.11 at the end of 15th year.

Money invested in eighth year will be saved for 7 years as they were invested at end of year 8 till end of year 15. It will become 6,000 (1 + 0.07)7 = 9,634.68 at the end of 15th year.

Money invested in ninth year will be saved for 6 years as they were invested at end of year 9 till end of year 15. It will become 6,000 (1 + 0.07)6 = 9,004.37 at the end of 15th year.

Money invested in tenth year will be saved for 5 years as they were invested at end of year 10 till end of year 15. It will become 6,000 (1 + 0.07)5 = 8,415.30 at the end of 15th year.

Additionally 8,626.1 was invested for 10 years which will become 8,626.1 (1 + 0.07)10 = 16,968.84

Sum of all payments is the amount which can be withdrawed at the end of year 15:

11,030.75 + 10,309.11 + 9,634.68 + 9,004.37 + 8,415.3 + 16,968.84 = 65,363.05