Bobby just turned 18, and he considers his role model to be Warren Buffett (who is exactly 72 years older than Bobby). Warren Buffett has a net worth today of $81 billion. Bobby wants to be an investor just like Buffett, and wants to be just as wealthy in exactly 72 years (in REAL terms) as Warren Buffett is now.

Bobby has a small part-time job mowing lawns, but still wants to start investing now. He plans to work for the next 52 years and contribute a portion of his salary each week to his investment account. During this time period, Bobby expects to earn a nominal 16.5% APR, compounded semi-annually, on his investments.

However, when he stops working in 52 years, hell transition to managing his investment account full-time. He will not withdraw any of the money (hell live from other sources of money). And Bobby believes that, with his full-time attention on his retirement funds, he can earn a nominal 24.0% APR, compounded semi-annually, on his investments for the remaining 20 years of his goal. Inflation is expected to be 1.4% APR, compounded quarterly.

Question: Bobby plans to start saving a little money, starting next week, and then grow it each week by 17.5% APR, compounded quarterly. How much would he need to contribute (in nominal terms) to the account next week in order to achieve his dream?