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If an amount of $1,000 \$$ is deposited into a savings account at an annual interest rate of 10%, compounded yearly, what the value of the investment after 30 DAYS?
Can anyone help me with this?
Is it enough to just do $A = (1 + r/n)^{nt}$ and convert $t$ to days instead of years?
I did that, $1000\times(1+0.1/1)^{30/365}$, and I get $1007.36$. But plugging the same values in this calculator gets me the result $1008.22$. Which is correct? What am i doing wrong?

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    $\begingroup$ Maybe I'm crazy, but if the interest is compounded yearly, does that mean you still have just $1000 after 30 days? The interest hasn't been compounded yet. $\endgroup$
    – littleO
    Dec 15 '17 at 9:38
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The correct answer is given by the calculator. In your case the compounding period is bigger than the saving period. Then it is common to use the simple interest.

$$C_{30}=1000\cdot \left(1+0.1\cdot \frac{30}{365}\right)=1,008.22$$


Similiar case if the saving period is not a multiple of the compounding period. Let´s say the saving period is $400$ days and the compound period is still $365$ days.

The first $365$ days it is compunded with $10\%$. Then for the remaining $35$ you use the simple interest.

$$C_{400}=1000\cdot 1.1\cdot \left(1+0.1\cdot \frac{35}{365}\right)=1,110.55$$

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  • $\begingroup$ Nice that correct answers are downvoted, without any reasoning. $\endgroup$
    – callculus
    Dec 19 '17 at 3:21
  • $\begingroup$ I suppose it's because your answer is wrong an the right answer is the comment of littleO: "if the interest is compounded yearly, does that mean you still have just $1000 after 30 days? The interest hasn't been compounded yet." $\endgroup$
    – alexjo
    Dec 19 '17 at 11:32
  • $\begingroup$ @alexjo I don´t think so. Try out the linked calculator in the question. Also I expect a comment if someone is downvoting an answer at first. $\endgroup$
    – callculus
    Dec 22 '17 at 16:33
  • $\begingroup$ you're assuming that the web calculator is right...but it isn't. Why should we switch from compound interest to simple interest (and with the same interest rate)? $\endgroup$
    – alexjo
    Dec 22 '17 at 19:58
  • $\begingroup$ @alexjo Yes I think the web calc is right. See also ask-math. There must be a difference if someone has deposited the money 2 years or 2 years and 4 months, for instance. I don´t know why so many people are so fast and strict in their judgments. $\endgroup$
    – callculus
    Dec 23 '17 at 13:54

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