Question

PLEASE ANSWER ASAP!! THANKS

A bond with a coupon rate of 5.32 percent and semiannual coupon payments matures in 16 years. The YTM is 6.49 percent. What is the effective annual yield?

A 10-year annuity making quarterly payments of 2250 will make its first payment 11 years and 3 months from today. You would like to purchase this annuity 2 years from today. If you want to earn an effective annual rate of 8.5% what should you be willing to pay 2 years from now? Enter your answer below to the nearest dollar.

Answer 1

1. YTM = 6.49%

Effective annual yield = (1 + YTM/2)^2 - 1

Effective annual yield = (1 + 0.0649/2)^2 - 1

Effective annual yield = 1.03245^2 - 1

Effective annual yield = 1.0659530025 - 1

Effective annual yield = 0.0659530025

Effective annual yield = 6.59530025%

2. We need to find the present value of the annuity as of 2 years from now

Effective quarterly rate, r = (1 + 0.085)^(1/4) - 1

r = 0.02060439584

n = 10 * 4 = 40 quarterly payments

PMT = 2250

This formula gives the present value one period before the first payment.

Now, we will discount this by (11 - 2) = 9 years to get PV2

PV2 = PV11/(1 + effective annual rate)^n

n = 11 - 2 = 9

PV2 = 60,902.431985601/(1 + 0.085)^9

PV2 = 60,902.431985601/2.0838557068

PV2 = $29,225.8392876557

We would be willing to pay $29,226 for this annuity in 2 years from now