Annuities of a non-annual time span

I am having trouble answering this question with any confidence and have no way to check my answer. I was hoping for a walk-through?

I plan to save $100 at the START of each month for the next two years. How much will I have at the end of the two year period (to nearest cent) if interest remains at 7% per annum (compounded monthly)? Thanks in advance! migrated from quant.stackexchange.comJun 22 '13 at 15:08 This question came from our site for finance professionals and academics. • This looks suspiciously like a homework question -- no one needs an answer to the nearest cent for their personal financial planning. – Mike Scott Jun 22 '13 at 15:17 • Well, it's not an annuity question, it's a simple time value of money. And yes, homework. Although, to the penny is ok. It at least lets us verify we are all calculating the same way. – JoeTaxpayer Jun 22 '13 at 16:19 • @User5580 - what have you tried to do? Calculator? Pencil? Spreadsheet? – JoeTaxpayer Jun 22 '13 at 16:20 1 Answer Your periodic interest rate is 0.07/12 = 0.005833333. You save$100 at the beginning of each month.

When is the interest posted? Let's say at the end of the month, before you make your next savings deposit.

So at the beginning of month 1, you have $100. At the end of month 1, you have$100 times 1.005833333, or $100.58. At the beginning of month 2, you have$100.58 plus your new deposit, giving you $200.58. At the end of month 2, you have$200.58 times 1.005833333, or $201.75. Rinse and repeat until you get to the end of month 24. Now, I don't know what assumptions are made about where the fractions of pennies go, or out to how many decimals the balance is kept. Answers may be off by a few cents if my assumptions aren't the same as yours. (I'm resolving the balance to the nearer cent when the interest is posted at the end of the month.) • +1 for excellent, simple answer. For the non-US user, the 'rinse and repeat' is a reference to the way shampoo marketers increased sales, suggesting a second washing was needed. Here, it means continue the process until solved. No, there's no Excel Function "rinse and repeat." – JoeTaxpayer Jun 23 '13 at 14:13 • No, if your interest is compounded monthly, you can't divide an annual rate by 12 to get a monthly rate -- you have to use logs. This is easy to confirm --$100 invested for 12 months with 0.5833333% interest per month will be \$107.23, not 107.00. You want (10 ^ (log(1.07)/12))-1, which gives 0.565415% per month. – Mike Scott Jun 23 '13 at 16:13
• @MikeScott, that's not the way I learned it. My loan interest is calculated exactly this way. From my latest statement: APR / (Daily Periodic Rate) = 1.99 / 0.005452 = 365.004. "7% per annum (compounded monthly)" ends up being more than 7% effectively, because of the interest earned on the interest. – mbhunter Jun 23 '13 at 18:38
• In that case it's not 7% per annum, even if it's quoted that way. In this case, it's 7.23% per annum. – Mike Scott Jun 23 '13 at 19:14