25-year, $1,000 par value bond has an 8.5% annual coupon The bond currently sells for $875 If the yield to maturity remains at its current rate, what will the price be 5 years from now?

Question

Quizplus · Accepted Answer

The bond currently sells for $875, which is less than the par value of $1,000. This indicates that the bond is selling at a discount.

We can use the formula for the present value of a bond to calculate its price in 5 years:

PV = C * [1 - (1 + r)-n]/r + FV/(1+r)n

Where:
PV = present value (price) of the bond in 5 years
C = annual coupon payment = 8.5% of $1,000 = $85
r = yield to maturity (assumed to be constant at the current rate)
n = number of years until maturity = 30 - 5 = 25
FV = par value of the bond = $1,000

Substituting the values:

PV = $85 * [1 - (1 + 0.085)-25]/0.085 + $1,000/(1+0.085)25 
PV = $85 * 12.5786 + $442.47 
PV = $1,079.47

Therefore, the price of the bond in 5 years is expected to be $1,079.47 (more than the current price of $875), which is closest to option C ($882.90).

25-Year, $1,000 Par Value Bond Has an 8