Question

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Answer 1

Face value, M = $ 10,000

Price of bond, P= $ 8,128

Coupon rate, C = 12% of $ 10,000 = $ 1,200

Required rate of return, i = 25%

Time, n = ?

The value of a bond is given we have to find the number of years. The value of a bond can be determined using the following formula

$\large P = C (P/A,i\%,n) + M(P/F,i\%,n)$

$\large 8,128= 1,200(P/A,25\%,n) + 10,000(P/F,25\%,n)$

$\large \implies 8,128= \frac{1,200}{0.25} (1-\frac{1}{1.25^n})+ \frac{10,000}{1.25^n}$

$\large \implies 8,128= 4,800(1-\frac{1}{1.25^n})+ \frac{10,000}{1.25^n}$

$\large \implies 8,128= 4,800-\frac{4,800}{1.25^n}+ \frac{10,000}{1.25^n}$

$\large \implies 8,128 - 4,800 = \frac{10,000 - 4,800}{1.25^n}$

$\large \implies 3,328= \frac{5,200}{1.25^n}$

$\large \implies 1.25^n= \frac{5,200}{3,328}$

$\large \implies 1.25^n= 1.5625$

Now taking log on both sides we get

$\large \implies nlog1.25= log1.5625$

$\large \implies n=\frac{ log1.5625}{log1.25}$

$\large \implies n=\frac{0.19382}{0.09691}$

$\large \implies n= 2$

No. Of years = 2

The value of bond for 2 years is $ 8,128.

Thus the investor must invest for 2 years in order to earn a return of 25%.

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