2) Solve the following NPV problems:

Problem 1 . Suppose that a borrower receives a 1,000 euro loan from Bank A, with a 10-year maturity at an annual interest rate of 5% with the obligation to pay the interest at the end of each year for the next 10 years. However, at the end of the 6th year, due to financial difficulties, he borrows from the same bank an additional 1,000 euros at an annual interest rate of 5% making the following agreement: a. not to pay any installment at the end of the next two years, i.e. the 7th and 8th year, and b. then pay an equal amount of interest for the next 8 years (i.e. from the end of the 9th year until the end of the 16th year) in order to fully repay the first as well as the second loan. It is requested to calculate the interest-rate installment of the loan that occurred after the restructuring.

Problem 2. Suppose that parents make family planning to finance their child's studies and buy a car. The expected costs for studies are EUR 10 000 per year that must be paid at the end of the 9th, 10th, 11th and 12th year from today. They also estimate that in 20 years from now (i.e. t 20) they will need to replace their large family car with a smaller one that will better serve them and estimate the cost to be EUR 15 000. For this reason they are determined to save a sum at the end of each year for the next 6 years in order to collect the necessary amount for both their child's studies and the car purchase. Note that the amount that they will save at the end of each year in the first three years will double in the next three years, i.e. at the end of the 4th, 5th and 6th years, respectively. It is asked to calculate the capital that they will have to save each year, assuming the annual interest rate is 5% and will remain constant for the next 20 years.