How much is a bond that pays $20 in coupon payments for 4 years and $1,000 at the end of the fourth year worth if the interest rate is 5%?

Question

Quizplus · Accepted Answer

To find the value of the bond, we need to calculate the present value of all the future cash flows. We can use the formula:

PV = C / (1+r)^n

Where PV is the present value, C is the cash flow, r is the interest rate, and n is the number of periods.

The coupon payments are $20 for 4 years, so the present value of those payments is:

PV of coupons = $20 / (1+0.05)^1 + $20 / (1+0.05)^2 + $20 / (1+0.05)^3 + $20 / (1+0.05)^4

PV of coupons = $72.17

The final payment of $1,000 at the end of the fourth year has a present value of:

PV of final payment = $1,000 / (1+0.05)^4

PV of final payment = $822.70

The total present value of the bond is the sum of the present value of the coupons and the present value of the final payment:

PV of bond = $72.17 + $822.70

PV of bond = $894.87

Therefore, the bond is worth $894.87, which is closest to answer choice B ($893.62).

How Much Is a Bond That Pays $20 in Coupon