Test Index

Time Value of Money

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Question : 17 of 99

Marks: +1, -0

What is the annual rate of interest compounded annually doubles an investment in 2 years. Given that

\sqrt{2}=1.4142135

$46.04125\%$
14.142135
$41.42135\%$
None

Solution:

Concept:

The doubling time formula for compound interest:

A = P(1 + r)^t

.

Explanation:

Let the principal be

P

and the amount after 2 years be

2P

.

Using the formula

A = P(1 + r)^2

, we get

2P = P(1 + r)^2

.

Cancel

P

:

(1 + r)^2 = 2

.

Take square root:

1 + r = \sqrt{2} = 1.4142135

.

Thus

r = 1.4142135 - 1 = 0.4142135

.

Convert to percentage:

r \times 100\% = 41.42135\%

.

Answer:

41.42135\%

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