(a) Once Sam received the prize, he will rent out his shop for $100,000 every three months, payable in advance on 1 January 2020 for travelling around the Europe. He then immediately invests half of each rental income into a fund paying 13% compounded quarterly. How much will be in the fund as on 31 December 2024?

(b) Sam is planning to arrange a tailor-made bank deposit investment plan that can generate a regular annual interest income of $35,000, starting with the first payment received 6 years from now and the last payment received 15 years from now. Calculate the present value of this annuity amount at Year 3, given the relevant discount rate is 12% per annum.

(c) If Sam is attracted by another investment compounded quarterly that grow 50% in 4 years, calculate the annual interest rate (APR) and effective annual rate (EAR) being earned for the investment.

(d) Sam invests $200,000 at Bank A that earns an annual interest rate of 12% compounded monthly. His wife puts $220,000 at Bank B with an annual interest rate of 6% compounded monthly. How long does Sam take to accumulate his account at bank A to arrive a doubled accumulated amount of his wife's at bank B?