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Future Value Question-Get your calculator!?

• I have a simple future value question (so I thought). If you put $510 in a savings account at the beginning of each year for 30 years, how much will be in the account at the END of the 30th year. The account earns 5%. I put N=30, I=5%, PV=0, PMT=$510 and got $33,883.81 as the future value, however, this is wrong. That will be the value on the first day of the 30th year. So then I changed N to 31 and subtracted the $510 payment on the first day of the 31st year. By doing this I got $35,578 as the value at the END of the 30th year. Is my logic right by doing it this way? Is that going to be the value at the END of the 30th year? Thanks in advance!

• Answer:

  I think your logic works and the correct answer is $35578.00. Another way to calculate it would be to take the $33,883.81 that you got for the value after the deposit at the beginning of year 30 and multiply it by 1.05 (to account for the 5% interest it will earn during the 30th year). To verify, I used a spreadsheet to calculate for each year. Column A has the value of column B for the previous year + 510 to account for the deposit at the beginning of the year and column B has the value of column A for the current year * 1.05 to account for the interest during the year. In year 30, column B has $35,578.00 which seems to confirm that your logic and my logic above are both correct ways to calculate it. What the first answerer actually calculated was the value at the end of the 29th year, which is not what you want.