Dr. Rafael Godoy decides to donate for a Natural Disasters Fund that aims to support the states of the Mexican Republic in the prevention and recovery of the effects produced by a natural phenomenon such as earthquakes, volcanic eruptions, tsunamis, etc.). This donation will be made with multiple contributions according to the following scheme of two stages:

Stage 1.Quarterlycontributions of constant amountforfive years, which will be paid at the end of each quarter. The first contribution will occur in two years and one quarter counted from today.

Stage 2.Subsequently, increasing annualcontributions every two years, that is, the contributions will remain constant every two years and will grow to 2% the following year, in order to remain constant again for two years. The first contribution will be made at the end of year 10. In addition, the first annual contribution will be for an amount equal to three times the amount of the quarterly contribution that will be paid in the first stage. If we denote by Z the amount of the first contribution that will be made in the second stage, the contribution scheme is as described below:

The first and second contributions will be equal to the amount Z. Subsequently, the contribution will grow 2% and will remain constant for two years, that is, the third and fourth contributions will be equal to the amount Z(1+0.02). Then the contribution will grow again 2% and will remain at that level for two years, that is, the fifth and sixth contributions will be equal to the amount Z(1+0.02)2, and thus the contributions will continue to grow successively in perpetuity.

The opportunity cost of capital will be 5% nominal annual with continuous capitalization during the first 10 years, and subsequently it will remain at 10% nominal annual with semiannual capitalization.

a)Ifthe amount of the first contribution of the second stage is Z = $100,000, calculate the present valueas of todayof the contributions of stage 1.

b)Ifthe first contribution of the second stage is Z = $100,000, calculate the total value of the donationas of today.

c)Assuming now that Dr. Rafael Godoy has today an amount of $1,500,000 to make the donation, calculate the amount Z of the first contribution of the second stage.