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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?

Clarinetist
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Nissan
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    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. – littleO Dec 15 '17 at 09:38

1 Answers1

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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.

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

callculus42
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  • Nice that correct answers are downvoted, without any reasoning. – callculus42 Dec 19 '17 at 03:21
  • 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." – alexjo Dec 19 '17 at 11:32
  • @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. – callculus42 Dec 22 '17 at 16:33
  • 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)? – alexjo Dec 22 '17 at 19:58
  • @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. – callculus42 Dec 23 '17 at 13:54
  • Actually, from a mathematical point of view, we ear interest only if we reach the compounding period. Otherwise, we don't. In the bank practice for the fractional part of the compounding period, we may find the use of simple interest, continuous compounding, daily compounding...So in general, the web site is wrong and so is your answer...The OP states "compounded yearly". Why shall we switch to simple interest? and why not to continuous compounding? or monthly compouding? or weekly compounding? or daily compounding?? – alexjo Dec 23 '17 at 19:51