For calculating the Effective Annual Rate (EAR) from various stated interest rates, I'm using the formula:
$EAR= \left(1+\frac{r}{p}\right)^{pt}-1$
where,
$p$ = no. of payouts in a period,
$t$ = no. of compounding periods (typically years),
$r$ = stated interest rate
So, if I have \10,000$ to invest for one year and the scheme says it will pay annual interest at $10$%, compounded quarterly, then for this situation:
$p$ = $4$ (since it is compounded quarterly),
$t$ = $1$ (I'm investing it for one year only),
$r$ = $0.1$ (@ $10$%)
and my EAR is calcutalted as EAR=\left(1+\frac { 0.1 }{ 4 }\right)^{ 4\cdot1 }-1= 10.38\%$
Questions:
What will be the values in the EAR equation for the following scenarios (I need to see the values to plug into the equation, not results, which I can obtain from a financial calculator):
- Period is 9$ months instead of one year, nominal rate is 10% per 9 months, and compounding is done thrice in the period.
- Period is 7 months instead of one year, nominal rate is 10% per 7 months, and compounding is done every 14 months (i.e. double period compounding)
- Period if 1 year, stated rate in 10% per year, but compounding is done every 2 years, not every year.
Thank you.