Math Help - Interest Rate

1. Interest Rate

I would be grateful for some help with this question.

Bank A offers to pay continuous interest on your savings with the time dependent interest rate $r(t)= 0.001(1+sin{\pi t})$. Bank B with time dependent rate $r(t)=0.07 \exp^{0.1t}$ and C with constant rate $r(t)=0.68$ where t denotes time in units of years. you want to fix your saving for one year. which offer should you choose? for the best offer, what do you have in your account after 1 year if you intially deposited £1000?

2. Are you sure you wrote those correctly? They are orders of magnitude different! Why would it be hard to choose?

If you change the sine to 0.01 and the constant to 0.068, the are a little closer, but still not a very interesting problem.