please solve this problem without using excel and show all steps.

4 A corporation has an obligation to repay a loan 5 years from now at a cost of 100,000. The present value of this obligation (based on the 5-year spot rate) is 76,513.44. The company will purchase bonds to support this liability. The available bonds are 3-year and 8-year zero-coupon bonds that are currently priced at 88.39 and 60.88 (per 100 of maturity value), respectively. What is the total face amount of the bonds that the company needs to purchase so that the present value and modified duration of its bond assets will match the present value and modified duration of its liability? A) 97,250 B) 100,000 C) 100,250 D) 102,250 E) 105,250