You want to save money to meet two goals.

• First, you would like to be able to retire 30 years from now with a retirement income of $100,000 per year for 25 years, with the first payment coming 31 years from today and the last 55 years from today.
• Second, you would like to pay for your grandchilds college education. The tuition payment will be $40,000 per year for four years. The first tuition payment will be 35 years from today and the last payment will be 38 years from now.
• You just won the lottery which will pay you $20,000 today (i.e., at year 0). These proceeds will help you meet the goals outlined above.

a) If you can earn on your investments a 16% EAR, how much will you have to save each year for the next 30 years, with the first saving amount starting in one year, and the last saving amount in 30 years?

b) Now assume you want to make quarterly contributions, instead of annual contributions, to meet your goals. You will begin saving an amount to meet your goals one quarter from today. How much will you need to save each quarter for the next 30 years to meet your goals? (Your last contribution is at the end of 30 years, and you can earn on your investments a 16% EAR).

how do you solve without excel?