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So, I am trying to figure out how to formulate this question.

Q: Alex and Anna each need £10 per week to live on. They decide to ask their dad for a weekly allowance. Alex agrees that she will receive £10 each week for one year (52 weeks). Anna notes that she could receive 3% per annum effective interest if she puts money in a savings account and then took out £10 from the account each week. She therefore asks for £500 at the start of the year instead. The first £10 (i.e paid to Alex and paid out by Anna) is at the end of the first week.

a) Does Anna end the year in surplus or does she run out of money. And if she does end in surplus how much would it be at the end of year?

I keep getting £512.24, but this makes no sense as it has to be in surplus with the way the question is worded.

Any help is greatly appreciated!

Mathsnovice
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  • I have more or less the same result. Anna runs out of money and at the end of the year she has a (negative) balance of $- 12.50$. – callculus42 Nov 04 '19 at 17:46
  • But how does that make sense when the question is quite forcing in telling you Anna has a surplus by asking you how much the surplus is? – Mathsnovice Nov 04 '19 at 18:10
  • "And if she does end in surplus ..." – callculus42 Nov 04 '19 at 18:17
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    There is an assumption being made that her interested is accrued weekly, but the various other possibilities are not going to make much difference. Anna should have asked for £520, like Alex, and kept her £8.1 profit. – Paul Sinclair Nov 05 '19 at 00:36
  • @PaulSinclair "Anna should have asked for £520, like Alex, and kept her £8.1 profit". That´s true. – callculus42 Nov 05 '19 at 16:54
  • @callculus - it didn't actually occur to me that Mathnovice may not have noticed that Anna received £20 less allowance than Alex until after I'd posted that comment. – Paul Sinclair Nov 05 '19 at 17:11

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