Shing and Benjamin, two classmates at a college, decided to use their free time after classes to create video games. On October 07, 2016, they received a loan of $3000 from a bank at 8.5% p.a. to start their small business. Two months later, they launched their first game in the community and it was highly successful. On March 02, 2017, a larger gaming company paid them $50,000 to purchase copyrights to their game. Shing and Benjamin used $5000 from this amount to settle the bank. loan and to cover other miscellaneous expenses.They then shared the balance of $45,000 equally between themselves. Shing invested a portion of it in a 182-day T-bill that had an interest rate of 4% p.a. and a face value of $7500 and used the balance in a 270-day interest-bearing promissory note at 6% p.a. Benjamin, on the other hand, invested a portion of it in a 270-day non-interest-bearing promissory note that had an interest rate of 5% p.a. and a face value of $9000, and loaned the balance to his friend, who was running a successful website-design business, for 182 days.

a.Calculate the total amount they paid to settle the bank loan.

b.i) Calculate the amounts that Shing invested in the T-bill and in the interest-bearing promissory note.

ii) Calculate the amount that Benjamin invested in the non-interest-bearing promissory note and the amount that he loaned to his friend.

c. Shing decided to discount his interest-bearing promissory note at the time of maturity of his T-bill (182 days) and used the money to purchase a car for himself. Calculate the total proceeds from his investments if he discounted his interest-bearing promissory note at 6.50% p.a.

d.Benjamin wants to have the same amount as Shing in 182 days. If he discounts his non-interest-bearing promissory note at 7% p.a., what interest rate should he charge his friend for the loan?

e.If Benjamin invested his initial share at the interest rate that he loaned to his friend (determined from (d)), how long would it take for his investment to double?