Make a time graph, with a focal time at 60 years.
My interpretation:
There will be 30 annual deposits of 50,000, then 5 withdrawals of x followed by
15 withdrawals of 530,000
Pick a focal point at age 60, and reduce all payments by a factor
of 1000 to keep the numbers smaller
amount of her 30 deposits = 50(1.09^30 - 1)/.09 = 6,815.376927 thousands
present value of her 15 withdrawals of 530 at age 60
= 530(1 - 1.09^-15)/.09 (1.09)^-5 = 2,776.614035 thousands
amount available for her at age 60 = 6,815.376927 - 2,776.614035 = 4,038.762892
This becomes the "present value" of 5 annuities of x
x(1 - 1.09^-5)/.09 = 4,038.76...
x = 1,038.335475 thousands or 1,038,335.48 Ksh.
Checking by doing it another way again reducing all monies by a factor of 1000:
let focal time be at age 80 (when she should run out of money)
value of her 30 deposits then = 50(1.09^30 - 1)/.09 (1.09)^20 = 38,196.17184
at age 80, value of her last 15 withdrawals = 530(1.09^15 - 1)/.09 = 15561.2856
value of her travel money at age 80
= 38,196.17184 - 15561.2856
= 22,634.88624
at age 80, value of her 5 withdrawals of x
= x(1.09^5 -1)/.09 (1.09^15) = x(21.79920342)
thus: x(21.79920342) = 22,634.88624
x = 1,038.335475 thousands = 1,038,335.48
One more try: focal point now
pv of deposits = 50(1-1.09^-30)/.09 = 513.6827022
Pv of her final 15 deposits = 530(1 - 1.09^-15)/.09 (1.09^-35) = 209.2765544
pv of her 5 withdrawals of x = x(1 - 1.09^-5)/.09 (1.09)^-30 = x(.293167434)
x(.293167434) + 209.2765544 = 513.6827022
x = 1,038.335475 thousands = 1,038,335.48 , wow! looks like I have the right answer
Assume that your friend Mary is 30 years old and wishes to provide for her retirement. Suppose that she invests Ksh. 50,000 per year at an interest rate of 9% per annum for the next 30 years with the 1st deposit accruing one year from now. At the age of 60 she will tour around the world for five years and on returning to Kenya, she wants to withdraw Ksh. 530,000 per annum for the next 15 years. Assuming that the 9% return remains constant, compute the maximum amount she can consume each year during her world tour. (10 Marks)
2 answers
I dont understand which formulae you used to get the answer for the 15 withdrawals
3 answers