Question

6,7 pls

6. A person deposits $1,000 in an account each year for five years beginning at the end of year 1). At the end of the fifth year (immediately after the deposit), one half of the account balance is withdrawn. $2,000 is deposited annually for five more years (starting at the end of year 6), and the total balance is withdrawn at the end of the 15th year. There are no additional deposits made in years 11 - 15. a. If the account earns interest at the rate of 8% per year, how much is withdrawn at the end of five years? b. If the account continues to earn interest at the rate of 8% per year, how much is withdrawn at the end of 15 years? 7. A sum of $100,000 is deposited now (time 0). The annual interest rate is 8% per year. The following end of year withdrawals will be made and the account will be empty after the fifth withdrawal EOY 1 23 Withdrawal $X $20,000 $20,000 $20,000 $20,000 How much is withdrawn at the end of the first year?

Answer 1

ANSWER:

6) I = 8%

A) Amount withdrawn after 5 years = deposit each year for 5 years(p/a,i,n) / 2

A = 1,000(F/A,8%,5) / 2

A = 1,000 * 5.867 / 2

A = 5,867 / 2

A = 2,933.5

so amount withdrawn after 5 years is $2,933.5

B) Amount withdrawn after 15 years = amount left after 5 years(f/p,i,n) + deposit from year 6 to year 10(f/a,i,n)(f/p,i,n)

A = 2,933.5(F/P,8%,10) + 2,000(F/A,8%,5)(F/P,8%,5)

A = 2,933.5 * 2.159 + 2,000 * 5.867 * 1.469

A = 6,333.42 + 17,237.24

A = 23,570.67

So amount withdrawn after 15 years is $23,570.67

7) I = 8%

Amount deposited in year 0 = $100,000

pw = cash flow in year 1(p/f,i,n) + cash flow from year 2 to year 5(p/a,i,n)(p/f,i,n)

100,000 = x(p/f,8%,1) + 20,000(p/a,8%,4)(p/f,8%,1)

100,000 = x * 0.9259 + 20,000 * 3.312 * 0.9259

100,000 = 0.9259 x + 61,331.61

100,000 - 61,331.61 = 0.9259 x

38,668.38 = 0.9259 x

x = 38,668.38 / 0.9259

x = 41,763.02

so the amount withdrawn after 1st year is $41,763.02