Test Index

Time Value of Money

© examsnet.com

Question : 21 of 99

Marks: +1, -0

A company sets aside a sum of

\text{₹}\,45,000

annually for 9 years to pay off a debenture issue of

\text{Rs.}\,5,00,000

. If the fund accumulates at

6\%

p.a., find the surplus after full redemption of the debenture issue.

$\text{₹}\,15,500$
$\text{Rs.}\,16,500$
$\text{₹}\,17,109$
None

Solution:

Concept:

Future value of an annuity and surplus calculation.

Explanation:

The company deposits ₹45,000 at the end of each year for 9 years into an account earning 6% p.a.

The future value of an ordinary annuity is given by:

FV = P \times \frac{(1+r)^n - 1}{r}

where

P = 45000

,

r = 0.06

, and

n = 9

.

Compute

(1.06)^9 = 1.689478958

Then

\frac{1.689478958 - 1}{0.06} = \frac{0.689478958}{0.06} = 11.49131597

Multiply by

P

:

45000 \times 11.49131597 = 517109.22

The debenture amount is ₹5,00,000.

Surplus =

517109.22 - 500000 = ₹17,109.22 \approx ₹17,109

.

Answer:

₹17,109.

© examsnet.com

Go to Question:

Prev Question

Next Question