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
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.