Test Index

Time Value of Money

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Question : 18 of 99

Marks: +1, -0

Ram is confused whether to invest at

9\%

p.a. compounded monthly or

9.25\%

p.a. simple interest, given that

(1+0.0075)^{12}=1.09380690

The student decided to find effective rate of interest which is

$9\%$
$9.25\%$
$9.38\%$
None

Solution:

Concept:

Effective annual rate is the equivalent annual interest when compounding is done more than once a year.

Explanation:

Given nominal rate

r = 9\% = 0.09

, compounded monthly (

n = 12

).

Effective rate

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

.

Monthly rate

= \frac{0.09}{12} = 0.0075

.

\left(1 + 0.0075\right)^{12} = 1.09380690

is given.

Thus effective rate

= 1.09380690 - 1 = 0.09380690

.

Convert to percentage:

0.09380690 \times 100\% = 9.38069\% \approx 9.38\%

.

Answer:

The effective rate is

9.38\%

.

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