If the letters have usual meanings, the formula for finding compound interest, compounded yearly for the given time is :

$1\dfrac{1}{2}$ years :

1. $P\Big[\Big(1 + \dfrac{r}{100}\Big)^{1\dfrac{1}{2}}- 1\Big]$

2. $P\Big(1 + \dfrac{r}{100}\Big)\Big(1 + \dfrac{r}{200}\Big)$ - P

3. $P\Big(1 + \dfrac{r}{200}\Big)^3$

4. $P\Big(1 + \dfrac{r}{100}\Big)^3\Big(1 + \dfrac{r}{200}\Big)- P$

If the letters have usual meanings, the formula for finding compound interest, compounded yearly for the given time is :

1 year :

1. $P\Big(1 + \dfrac{r}{100}\Big)^1 - P$

2. $P\Big(1 + \dfrac{r}{200}\Big)$ - P

3. $P\Big(1 + \dfrac{1}{200}\Big)^2$ - P

4. $P\Big(1 - \dfrac{r}{200}\Big)^2$ - P

When interest is compounded half-yearly then the formula for C.I. for the given time is :

1 year :

1. $P\Big(1 + \dfrac{r}{200}\Big)^2 - P$

2. $P\Big(1 + \dfrac{r}{100}\Big)^2 - P$

3. $P\Big(1 + \dfrac{r}{200}\Big)^2$

4. $P\Big(1 + \dfrac{r}{100}\Big)^2$

When interest is compounded half-yearly then the formula for C.I. for the given time is :

$1\dfrac{1}{2}$ years

1. $P\Big(1 + \dfrac{r}{200}\Big)^{\dfrac{3}{2}} - P$

2. $P\Big(1 + \dfrac{r}{200}\Big)^3 - P$

3. $P\Big(1 + \dfrac{r}{100}\Big)^3 - P$

4. $P\Big(1 + \dfrac{r}{100}\Big)^{\dfrac{3}{2}} - P$