Test Index

Time Value of Money

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Question : 42 of 99

Marks: +1, -0

In what time will compound interest on

\text{Rs.} 320

12\;\frac{1}{2}\%

p.a. compounded annually be

\text{Rs.} 85?

$4\;\frac{1}{2}$ years
$2\;\frac{1}{2}\%$ Years
2 Years
5 Years

Solution:

Concept:

Use the formula for compound interest:

A = P(1 + r)^t

, where

CI = A - P

.

Explanation:

P = 320

,

r = 12\frac{1}{2}\% = \frac{1}{8}

,

CI = 85

.

A = P + CI = 320 + 85 = 405

.

So

320\left(1 + \frac{1}{8}\right)^t = 405

.

320\left(\frac{9}{8}\right)^t = 405

⇒

\left(\frac{9}{8}\right)^t = \frac{405}{320} = \frac{81}{64}

.

\frac{81}{64} = \left(\frac{9}{8}\right)^2

, hence

t = 2

years.

Answer:

2 years, which corresponds to option C.

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