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Hi I just want some verification that my answer is right if that's ok:

Question: Tim has \euro 1000. A bank offers to pay $5\%$ (pa) (payable quarterly). How long must Tim deposit the money so that she may withdraw \euro 1500.

Answer: $n_{min} = \frac{log_{10} (\frac{1500}{1000})}{log_{10}(1+0.0125)} = 33years$

Question:Jim has \euro 1600. A bank offers to pay $4\%$ interest (pa)(payable quarterly). How long must Jim deposit the money so he earns \euro 400 in interest?

Answer: $n_{min} = \frac{log_{10} (\frac{2000}{1600})}{log_{10}(1+0.01)} = 22years$

I'm fairly certain about the first one, but just want to make sure about the second - i.e that it was ok to not change around the formula somewhat.

Thank you

moony
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  • Not sure what is going on, I put answers in my question but it won't show it keeps saying.Math processing error. I won't write the formula out again but answer 1 I get 33 years, ans 2 I get 22 years – moony Feb 13 '16 at 00:17

1 Answers1

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You have a problem with both answers: $n$ is the number of compounding periods that have passed, not the number of years.

For the second, you correctly converted the problem to be of the same form as the first (Total value = principal + interest earned), so of course it is okay to use the same formula.

Paul Sinclair
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  • Ah yes ok so for example the 33years has to be divided by 4 = 8.25 years = 9 years? – moony Feb 15 '16 at 17:06
  • If Tim can't withdraw her money until the end of a year, then yes. however the money will be in the account after 8.25 years, since it is compounded quarterly. – Paul Sinclair Feb 15 '16 at 17:49