Test Index

Time Value of Money

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Question : 40 of 99

Marks: +1, -0

At what rate % will a sum double itself in 7 years if the interest is compounded annually.

$7.0\%$
$8.0\%$
$10.41\%$
$7.9\%$

Solution:

Concept:

Use compound interest formula:

A = P\left(1 + \frac{r}{100}\right)^t

, where

A

is the amount,

P

is principal,

r

is rate,

t

is time. For doubling,

A = 2P

.

Explanation:

Set up the equation:

2P = P\left(1 + \frac{r}{100}\right)^7

Cancel

P

:

2 = \left(1 + \frac{r}{100}\right)^7

Take the 7th root:

1 + \frac{r}{100} = 2^{1/7}

2^{1/7} \approx 1.10409

Thus

\frac{r}{100} = 0.10409

r = 10.409\% \approx 10.41\%

Answer:

The required rate is

10.41\%

per annum.

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