John Travolta, a young entrepreneur whose names betray his age but where the composition intervenes to restore the balance, wants to set up a business that he will finance by capital invested from his relatives and family. To found the company, JT, to name it to his kindness, must raise a tidy sum of $500,000. Its objective is to be able to put on foot the company in exactly 2 years. He found 4 investors ready to provide him with funds:

- His mom can offer him $250,000 now, which he will put in a capital savings account protected for 2 years at the effective monthly rate of 0.25%;

- His friend Jack, a faithful companion at heart, offers him to invest $400 per pay period in starting with a payment today. Jack is paid every fortnight (every 15 days) and JT will place all these amounts in his principal-protected savings account;

- His dad, an expert in finance, believes it's wiser to take care of the money himself. will be used to fund the business. The latter will offer him a sum of $ 10,000 per quarter the first sum of which will be invested at the beginning of the next quarter at the projected rate of 2% effective monthly;

- His girlfriend, who is in school and works part-time, thinks she will be able to raise $10,000 per year to give to him at the end of each year. JT will place this cash in its savings account with guaranteed capital each year when he receives the sum.

a) Considering this information, how much will they manage to accumulate to start the business at JT?

b) John Travolta already has $20,000, how much should he save each month, starting today, to achieve his goal? Consider that her cash will be managed by her daddy.