A company must pay a liability of $1,000 in 2 years. Zero coupon bonds with terms of 1 year and 4 years are available for investment. The effective rate of interest is 7.5%.

a. How much of each bond should the company buy in order to achieve full immunization?

b. Show empirically that immunization has been achieved even for large changes in the interest rate. Take as an example a decrease in the interest rate to 0% and an increase to 100%.

Could you help me solve this problem with full steps and without the use of a BA calculator? Thank you!