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Q.

A company wants to set up a sinking fund to pay off a bond issue of Rs. 1,00,00,000 after 10 years. The company can invest in a scheme that pays 8% interest compounded annually. What amount should be invested annually to accumulate the required sum? ( Rounded to nearest lakhs)

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a

7 Lakhs

b

9 Lakhs

c

8 Lakhs

d

4 Lakhs

answer is C.

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Detailed Solution

Face value of bond issue = Rs. 1,00,00,000 Time period = 10 years Interest rate = 8% compounded annually

The amount to be invested annually can be calculated using the following formula:

A = (S * r) / ((1 + r)^n - 1)

where A is the amount to be invested annually, S is the total sum required at the end of the time period, r is the interest rate, and n is the number of years.

S = Face value of bond issue = Rs. 1,00,00,000 r = 8% p.a. n = 10 years

A = (1,00,00,000 * 0.08) / ((1 + 0.08)^10 - 1) = Rs. 7,88,670.23 (approx)

Therefore, the company should invest Rs. 7,88,670.23 annually to accumulate the required sum.

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