Question

5 of 16 (4 complele) HW Score: Problem 4-62 (algorithmic) 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year for five years (starting at the end of year one) At the end of the fifth year, one-half of the account balance is withdrawn, 56,000 is deposited annually for five more your starting in the balance withdrawn at the end of the fifteenth year.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11-15 a. Choose the correct cash flow diagram b. If the account earns interest at the rate of 6% per year how much is withdrawn at the end of five years? c. If the account continues to eam interest at the rate of 6% per year how much is withdrawn at the end of 15 years?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 7-6% per year о А. OB EK 65K EXEK 1 2 3 4 5 6 7 8 9 10 11 12 13 F.12 C 17 :50 100 1212.10 Click to select your answer and then click Check Answer 2 parts

Answer 1

a) Option A is the correct cashflow diagram

Option A accurately depicts the cashflows given in the question.

b) Money withdrawn at end of 5-years

Future value of annuity= P [(1+i)n-1]/i

In our case, P = 3000, i= 0.06, n=5

So future value at end of 5-years= 3000[1.065-1]/0.06 = 16911.2788

Money withdrawn at end of 5-years =Future value at end of 5 years/2

= 16911.2788/2 = 8455.64

So at end of 5 years $8455.64 is withdrawn.

c) Money withdrawn at end of 15 years

At end of 5 years 8455.64 is left. Its future value at end of 15 years will be 8455.64 (1+0.06)10. ie 15412.76

Now, 6000 is deposted at annually from 5th year to 10th year, at end of each period

Its future value at end of 10 years will be = 6000[1.065-1]/0.06 = 33822.56

Now future value of above at end of 15 years will be 33822.56(1+0.06)5 ie 45262.21

So at end of 15 years person withdraws = 15412.76 + 45262.21

= 60674.97

So at end of 15 years $60674.97 is withdrawn.