Test Index

Time Value of Money

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Question : 77 of 99

Marks: +1, -0

What is the effective rate of interest if the nominal rate

5 \%

p.a converted quarterly?

$6.09 \%$
$5.09 \%$
$5.55 \%$
$5.60 \%$

Solution:

Concept:

Effective rate is the actual annual return when compounding occurs more than once per year.

Explanation:

Formula:

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

, where

r = 0.05

,

n = 4

.

Calculate

\frac{r}{n} = \frac{0.05}{4} = 0.0125

.

Compute

(1 + 0.0125)^4 = (1.0125)^2 \times (1.0125)^2

.

1.0125^2 = 1.02515625

.

1.02515625^2 = 1.050945

(approx).

Subtract 1:

0.050945 = 5.0945\% \approx 5.09\%

.

Answer:

5.09\%

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