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Answer:
Min number required = 36742.44878 rounded off to 36743 bonds
Explanation:
To calculate the minimum number of bonds that must be sold, we first need to calculate the bonds price.
To calculate the price of the bond today, we will use the formula for the price of the bond. We assume that the interest rate provided is stated in annual terms. As the bond is a semi annual bond, the coupon payment, number of periods and semi annual YTM will be,
Coupon Payment (C) = 1,000 * 0.062 * 6/12 = $31
Total periods (n) = 20 * 2 = 40
r or YTM = 0.0775 * 6/12 = 0.03875 or 3.875%
The formula to calculate the price of the bonds today is attached.
Bond Price = 31 * [( 1 - (1+0.03875)^-40) / 0.03875] + 1000 / (1+0.03875)^40
Bond Price = $843.7107767 rounded off to $843.71
The bonds will sell at a price of $843.71 today.
So the minimum number of bonds that must be sold is,
Min number required = 31,000,000 / 843.7107767
Min number required = 36742.44878 rounded off to 36743 bonds
