Test Index

Time Value of Money

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Question : 14 of 99

Marks: +1, -0

A company requires

\text{₹60,00,000}

after 5 years to redeem debentures. It is decided to create a sinking fund by investing a fixed amount every year in securities giving

10\%

compound interest. The yearly investment is [Given

(1.1)^{5}=1.6]

10,00,000
9,60,000
12,00,000
none

Solution:

Concept:

Sinking fund involves equal annual investments that grow with compound interest to meet a future liability.

Explanation:

Future value of annuity formula:

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

.

Given

FV = ₹60,00,000

,

r = 10\% = 0.10

,

n = 5

, and

(1.1)^5 = 1.6

.

Compute

\frac{(1.1)^5 - 1}{0.1} = \frac{1.6 - 1}{0.1} = \frac{0.6}{0.1} = 6

.

Thus

60,00,000 = A \times 6

⇒

A = \frac{60,00,000}{6} = 10,00,000

.

Answer:

Yearly investment is ₹10,00,000.

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