Question

you want to be able to withdraw $50,000 each year for 15 years. Your account earns 6% interest. a) How much do you need in your account at the beginning? How much total money will you pull out of the account? $ c) How much of that money is interest?

Answer 1

If we put x $ in bank now, we get $, where n is the number of years

assume we are at year, Y0 now.

to withdraw 50000 at end of first year, Y1, we need to put

to withdraw 50000 at end of second year, Y2, we need to put

and so on.

(a)

Thus, money that we put now

= 50000/(1+ 0.06)^1 + 50000/(1+ 0.06)^2 + 50000/(1+ 0.06)^3 + 50000/(1+ 0.06)^4 +

50000/(1+ 0.06)^5 + 50000/(1+ 0.06)^6 + 50000/(1+ 0.06)^7 + 50000/(1+ 0.06)^8 +

50000/(1+ 0.06)^9 + 50000/(1+ 0.06)^10 + 50000/(1+ 0.06)^11 + 50000/(1+ 0.06)^12 +

50000/(1+ 0.06)^13 + 50000/(1+ 0.06)^14 + 50000/(1+ 0.06)^15

= 485612.449387 $

(b) Money that we will take out = 50000*15 = 750000 $

(c) Interest = 750000 - 485612.449387 = 264387.550613 $