a) What is the duration of a mortgage with a fixed interest rate and a 30-year term if the loan value decreases from $ 100,000 to $ 89537 when the interest rate increases from 5% to 6%?

b) Calculate the duration of a loan with a value of $ 200,000 and a term of 4 years. The loan is repaid with annual interest payments of $ 16,000 and the entire loan value is repaid at the end of the term, the interest rate is 8%.

c) If the loans in a) and b) are the only ones included in the loan portfolio for an investor, what is the total duration of the loan portfolio?

d) How does the value of the loan portfolio change if the interest rate decreases from 5% to 4%? Answer in percent.