Barbara wants to save money to meet 2 objectives:

Question

i. She would like to be able to retire 25 years from now and have a pension for 15 years after that.She would like to get the first annual payment on the pension 26 years from now, she would like it to be $30,000 and she would like it to grow at the rate of 3% per year from then onwards (for15 years).

ii. She would also like to purchase a $25,000 car, 10 year from now.
The interest rate (cost of capital) Barbara can lend and borrow at is 6% per year. Assume she deposits the same amount S at the end of each year for 25 years, with the first deposit of annual savings being 1 year from now.

What is the amount S such that Barbara will exactly be able to meet her objectives (described in (i)
and (ii): pension plan and car)?