# What is the value of a principle after 30 DAYS for an annual interest compounded annually?

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? • 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. Dec 15 '17 at 9:38 ## 1 Answer 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.$$C_{400}=1000\cdot 1.1\cdot \left(1+0.1\cdot \frac{35}{365}\right)=1,110.55$$• Nice that correct answers are downvoted, without any reasoning. Dec 19 '17 at 3:21 • 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." 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. 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)? 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. Dec 23 '17 at 13:54