Answer:
Ans. The price of the bonds on December 31, 2021 discounted at 6% is $99,170,444
Step-by-step explanation:
Hi, we need to use the following formula to find the present value of the bond, which is the same as saying, discount all future cash flows to present value.
![Price=\frac{Coupon((1+r)^{n}-1) }{r(1+r)^{n} } +\frac{FaceValue}{(1+r)^{n} }](https://tex.z-dn.net/?f=Price%3D%5Cfrac%7BCoupon%28%281%2Br%29%5E%7Bn%7D-1%29%20%7D%7Br%281%2Br%29%5E%7Bn%7D%20%7D%20%2B%5Cfrac%7BFaceValue%7D%7B%281%2Br%29%5E%7Bn%7D%20%7D)
Where:
r= discount rate (in our case 6% or 0.06)
Coupon =$115,000,000*0.05=$5,750,000
n= periods of payment (in our case, 30 years or just 30)
Everything should look like:
![Price=\frac{5,750,000((1+0.06)^{30}-1) }{0.06(1+0.06)^{30} } +\frac{115,000,000}{(1+0.06)^{30} }](https://tex.z-dn.net/?f=Price%3D%5Cfrac%7B5%2C750%2C000%28%281%2B0.06%29%5E%7B30%7D-1%29%20%7D%7B0.06%281%2B0.06%29%5E%7B30%7D%20%7D%20%2B%5Cfrac%7B115%2C000%2C000%7D%7B%281%2B0.06%29%5E%7B30%7D%20%7D)
![Price= 79,147,779.12 +20,022,665.05=99,170,444.18](https://tex.z-dn.net/?f=Price%3D%2079%2C147%2C779.12%20%2B20%2C022%2C665.05%3D99%2C170%2C444.18)
The price of the bond to the nearest whole dollar is $99,170,444
Best of luck.