How would I do the following problem:
Jimmy opens a savings account with a X deposit at the beginning of the month. The account earns P% annual interest compounded monthly. At the beginning of each subsequent month, Jimmy deposits an additional $X. How much will the account be worth at the end of N years? I am specifically confused about annual interest compounded monthly means. Please help me. Thank you!
I am specifically confused about annual interest compounded monthly means. Please help me. Thank you!
Interest is usually compounded at the end of each year, and therefore the rates of interest are usually given per year (usually called per annum). However, interest can be compounded over any interval of time, no matter how small, just by using the appropriate rate, which comes from changing the unit of the annual rate to the appropriate measure of time. Thus, for example, if we have a rate of $r$ of the deposit per year, then since we have twelve months in a year, the same rate works out to $r/12$ of the deposit per month. That is, we distribute the yearly rate equally to the twelve moths composing the year.
Hope this helps.
