When interested is compounded the total time period is subdivded into several interest periods 1 year 3 months or 1 month how does compound interest effect the future value of an investment?

Answer 1

If the three-month interest rate was a quarter of the 12 month interest rate, then you would earn more interest. By extension, the shorter the subdivisions of time, the better off the investor would be.

But this calculation is based on dividing the annual interest by four for a three month period. That is how simple interest works, but not compound interest. No financial company is going to fall for that! Their 3-moth rate will be based, not on a quarter, but on the fourth root of the annual rate.

Thus, if the annual rate is r%

the quarterly rate will be 100*[(r/100 + 1)0.25 - 1] %

The calculation looks more complicated than it is due to (a) the need to convert percentage into fractions (why 100 crops up), and (b) to include the original capital to start off and then to exclude it (why the +1 and -1 come in).

So, if r = 4% annually, then the quarterly rate will not be 1% but 0.98534% (approx). If the exact figure were used, then the four quarters, compounded, would equal exactly 4%. But there are no bets on whether the deposit taker will round that fraction up or down!