Quick questions on Financial Mathematics - TCE Mathematics Applications (Tasmania)

Monthly compounding earns more (\9573.44$versus$\$9528.13$) because interest is added more often. The extra interest is \45.31$.

A recurrence relation defines each term from the previous one. This is the natural language of a spreadsheet or financial calculator.

To compare investments with different compounding frequencies, convert the nominal rate to an effective annual rate: $$r_{\text{eff}} = \left(1 + \frac{r_{\text{nom}}}{k}\right)^k - 1$$where$k$is the number of compounds per year. For the$6\%$monthly example,$r_{\text{eff}} = (1.005)^{12} - 1 = 0.061678$, or about$6.17\%$. This is why monthly compounding beats annual at the same nominal rate.