Test Index

Time Value of Money

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Question : 61 of 99

Marks: +1, -0

If the effective rate of interest is

12 \%

per annum and the interest is compounded quarterly, the nominal rate of interest per annum

$11.78 \%$
$11.21 \%$
$11.89 \%$
$11.49 \%$

Solution:

Concept:

The effective and nominal rates are connected by compounding frequency.

Explanation:

Let nominal rate be

r

per annum, compounded quarterly, so

n = 4

.

Effective rate

i = 12\% = 0.12

.

Formula:

i = \left(1 + \frac{r}{n}\right)^n - 1

.

Thus

\left(1 + \frac{r}{4}\right)^4 - 1 = 0.12

→

\left(1 + \frac{r}{4}\right)^4 = 1.12

.

Take fourth root:

1 + \frac{r}{4} = (1.12)^{1/4}

.

Compute

(1.12)^{1/4} \approx 1.02874

.

So

\frac{r}{4} \approx 0.02874

→

r \approx 0.11496 = 11.496\% \approx 11.49\%

.

Answer:

11.49\%

per annum, which is option D.

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