Question: Tom puts $10,000 into a bank account that pays an annual effective interest rate of 4% for ten years. If a withdrawal is made during the first five and one-half years, a penalty of 5% of the withdrawal amount is made. Tom withdrawals K dollars at the end of each of 4, 5, 6 and 7 years. The balance in the account at the end of year 10 is $10,000. Calculate K

Part of the calculations: If no withdrawals than total amount is 10K(1.04)^10 =$14802.42

$14802.42-$10000 = $4802.20 has been withdrawn

Withdrawals = $4802.20 = x(1.05) + x(1.05) + x + x

I know this is wrong, but how far wrong?

closed as off-topic by Dheer, Michael, Pete B., Nathan L, MD-Tech Oct 30 '17 at 13:09

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  • 3
    A homework problem? – RonJohn Oct 25 '17 at 15:53
  • 2
    Each withdrawal reduces future interest as well, so $4,802.20 is irrelevant. – Hart CO Oct 25 '17 at 16:12
  • That's what I thought. – Mark Oct 25 '17 at 16:15

This is the formula I came up with:

((((10000 x 1.04^4 - 1.05K) x 1.04 - 1.05K) x 1.04 - K) x 1.04 - K) x 1.04^3 = 10000

Solve for K.

  • The important question now is: do you know why I derived this equation? – RonJohn Oct 25 '17 at 16:29
  • Simultaneous equation. Observing the past into the future. – Mark Oct 26 '17 at 14:39
  • 1
    @Mark was I supposed to use simultaneous equations? :( I started at "year 0" and just followed the parameters set by the problem: four years of growth, then a year of growth and a deduction (including 5% penalty), then two more years like that, then three final years of growth. – RonJohn Oct 26 '17 at 15:00
  • Obviously not. There is no equation to the right. But those brackets get me everytime. Thank you. – Mark Oct 26 '17 at 21:44

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