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Answer:
X=97.24
Explanation:
PV = Present Value = X+2000 by the 16th years
PMT = Payments = $100
FV = Future Value = 2000 at the end of 16 years
n= number of years
Applying the equation of future value for annuity
FV = pmt* ((1+r)ⁿ - 1
)/r
Inputting the values;
2000=100*((1+r)¹⁶-1)/r
Solving for r, gives r = 2.9%
Therefore using the formula for PV for annuity;
PV=PMT*(1-(1/1+r)/r)
X=100*(1-(1/1.029)/0.029
X=100*((1-0.9718)/0.029)
X=100*(0.0282/0.029)
X=97.24
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Answer:
Bond Price = $951.9633746 rounded off to $951.96
Explanation:
To calculate the quote/price of the bond today, which is the present value of the bond, we will use the formula for the price of the bond. As the bond is an annual bond, we will use the annual coupon payment, annual number of periods and annual YTM. The formula to calculate the price of the bonds today is attached.
Coupon Payment (C) = 1000 * 10% = $100
Total periods remaining (n) = 3
r or YTM = 12%
Bond Price = 100 * [( 1 - (1+0.12)^-3) / 0.12] + 1000 / (1+0.12)^3
Bond Price = $951.9633746 rounded off to $951.96
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