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Mary got a loan of 1000 euros. The institution that made the loan charges a monthly fee of 1%.

Because, in the following 6 months, Mary has done no amortization of the loan, how much does she owe to the institution after those 6 months?

I could solve this problem 2 ways:

$$1000 \cdot e^{.01t} \approx 1061.84$$ or

$$1000 \cdot (1+.01)^6 \approx 1061.52$$

My book says the second one is correct, but since the values are so similar, are both solutions correct? If not, why?

Git Gud
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Mark Read
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    Your first version uses what is called "continuous compounding", which I find confuses more people than it helps. Your second answers the question, with $1%$ compound interest each month. They would be clearly different if you used a $100%$ monthly interest rate: $1000 \times e^t$ compared with $1000 \times 2^t$ – Henry Nov 10 '16 at 00:35
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    The first formula is for continuous compounding interest. The second is for discrete compounding interest, which is more appropriate for this scenario, because the fee is applied monthly. See this for more info. – 2012ssohn Nov 10 '16 at 00:36
  • If the answers are close enough can you please send all math.SE users $0.32. No bank in the world would say they are both correct. – Ian Miller Nov 10 '16 at 00:41
  • @IanMiller You'd be surprised. – Git Gud Nov 10 '16 at 00:43
  • Let me change 'would' to 'should' then. Or at least no bank I'd trust my money with. – Ian Miller Nov 10 '16 at 00:46

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