A hundred days of compounding

You deposit $100 into an account earning 1%1\% interest compounded daily. To the nearest dollar, how much is in the account after 100100 days?

Show hints (2)+
  1. Daily compounding: balance =100⋅(1.01)100=100\cdot(1.01)^{100}.
  2. (1.01)100≈2.70(1.01)^{100}\approx2.70, so about $270 (not the simple-interest $200).

Answer

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270

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