Question

Find the nominal rate compounded semi annually equivalent to 4.2 % effective rate of interest. Answer: 4.156%

Answer 1

Answer:

4.16%

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Answer 2

Given: Effective rate of interest ($r_{e}$) = 4.2%

To find: The nominal rate compounded semi annually equivalent to given effective rate of interest

Let: The nominal rate of interest be $r$

Solution: Given that,

Effective rate of interest ($r_{e}$) = 4.2% = 0.042

Number of conversion periods per year (m) = 2 (Interest is compounded semi-annually)

Nominal rate of interest ($r$) = ?

∵ $r_{e} = (1 + \frac{r}{m})^{m} - 1$

⇒ $0.042 = (1+\frac{r}{2}) ^{2} - 1$

⇒ $1.042 = (1+\frac{r}{2} )^{2}$

Taking root on both sides

⇒ $\sqrt{1.042} = 1 + \frac{r}{2}$

⇒ $1.02078 - 1 = \frac{r}{2}$

⇒ $r = 0.02078 \ * \ 2 = 0.04156$

⇒ $r = 4.156%$ %

Hence, nominal rate of interest is 4.156%.