Test Index

Time Value of Money

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Question : 5 of 99

Marks: +1, -0

In how many years would a sum be 3 times at

12 \%

rate of Compound interest? (Given

3^{\frac{1}{9.7}}=1.12

).

12 years
$\frac{1}{9.7}$ years
9.7 years
none

Solution:

Concept:

Use the compound interest formula

A = P(1+r)^n

and the given relation

3^{\frac{1}{9.7}} = 1.12

to find

n

.

Explanation:

Let the principal be

P

. The amount becomes

3P

at

12\%

compound interest per annum.

So

3P = P(1+0.12)^n

Cancel

P

:

3 = (1.12)^n

Take both sides to the power

\frac{1}{9.7}

:

3^{\frac{1}{9.7}} = (1.12)^{\frac{n}{9.7}}

But given

3^{\frac{1}{9.7}} = 1.12

, so

1.12 = (1.12)^{\frac{n}{9.7}}

Equating exponents:

1 = \frac{n}{9.7}

Thus

n = 9.7

years.

Answer:

9.7 years

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