Test Index

Time Value of Money

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Question : 4 of 99

Marks: +1, -0

The rate of interest on a sum of money is

8\%

p.a. for the first year,

6\%

p.a. for the next 4 years and

4\%

p.a. for the period beyond 5 years. If the simple interest accursed by the sum for a total period of 11 years is

\text{₹}1120

what is the sum?

$\text{₹} 2000$
$\text{₹} 3000$
$\text{₹} 4000$
$\text{₹} 5000$

Solution:

Concept:

Simple interest is proportional to principal, rate, and time.

Explanation:

Let the principal be

P

.

Interest for first year (8% for 1 year):

P \times \frac{8}{100} \times 1 = 0.08P

.

Interest for next 4 years (6% for 4 years):

P \times \frac{6}{100} \times 4 = 0.24P

.

Interest for remaining 6 years (4% for 6 years):

P \times \frac{4}{100} \times 6 = 0.24P

.

Total interest:

0.08P + 0.24P + 0.24P = 0.56P

.

Given total interest = ₹1120, so

0.56P = 1120

.

Thus

P = \frac{1120}{0.56} = 2000

.

Answer:

The sum is ₹2000.

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