Use Present Value ordinary annuity "PVoa"...
PVoa = PMT [(1 - (1 / (1 + i)^n)) / i]
= 50,000[(1 - (1 / 1.10^20)) / 0.10
= 50,000[(1 - 0.14864) / 0.10]
= 50,000[8.51356]
= $425,678.186, round to $425,678.19
2. A bond has the face value of $1,000, a coupon rate of 8% with a 2 year maturity. What is the price of this bond if the discount rate is 9%?
coupon (assuming semi-annual coupons are paid): 1,000 * 0.08/2 = $40
PV of the coupons (use PVoa):
n = 2 yrs * 2 coupons per year = 4, i = 0.09/2 = 0.045
= 40[(1 - (1 / 1.045^4)) / 0.045]
= 40[(1 - 0.83856) 0.045]
= 40[3.58753]
= 143.50
PV of par paid at maturity: 1,000/1.045^4 = 838.56
Add the two PVs together = price: $982.06
What happens to the price if the discount rate goes down to 8%?
If the discount rate is 8% and the coupon rate is 8%, the bond will sell at par: $1000
1. Calculate the present value of an annuity that pays $50,000 at the end of each year for 20 years. The discount rate is 10%
2. A bond has the face value of $1,000, a coupon rate of 8% with a 2 year maturity. What is the price of this bond if the discount rate is 9%? What happens to the price if the discount rate goes down to 8%?
I have trouble using correct formulas.
