Please also show steps! Thank you! 1.)A $10,000 T-bill with 238 days till maturi

Question

Please also show steps! Thank you!

1.)A $10,000 T-bill with 238 days till maturity is sold at a simple discount rate of 2.54%.   Find the price paid for this T-bill.

2.) The Titan Siren Company was due to receive a payment of $475,000 on March 3, 2012.   A finance company offered to buy this receivable on January 11, 2013 for $471,500.   Find the simple discount rate for this offer.

3.)An insurance agent has just sold a large policy and will be paid a commission of $3,279.46 in 20 days.   His brother-in-law offers to give him cash right now in exchange for his commission check for a fee of 3.5%.   What is the equivalent simple interest rate?

4.)A $5,000 simple discount bond which matured on December 1, 2011 was sold for $4,965.16.   The simple discount rate was 2.93%.  When did the sale take place?

5.)On April 1, 2013 the Cattarauqua Ginseng Company borrowed $40,000 for 100 days at 11.63% simple interest.   On May 12, 2013 the note was sold at a simple discount rate of 27.39%.   a) What was the selling price of the note?  (10 points)  b) What simple interest rate did the original lender earn?  (5 points)   c)   What simple interest rate did the company actually pay?

Explanation / Answer

1. D= MdT

10,000-Price = 10000*2.54%*238/365

Price= $9,834.38

2. Days between January 11, 2013 and March 3 = 51 days

475,000-471,500 = 475,000*d*51/365

d= 5.27%

simple discount rate = 5.27%

3.Interest= 3.5%*3,279.46=114.7811

114.7811 = 3,279.46*i*20/365

i= 63.88%

4. D= MdT

5,000-4,965.16 = 5000*2.93%*t/365

t= 86.80 days or 87 days

Sales took place on September, 5 2011

5.

Maturity value of note = 40,000*11.63%*100/365 + 40000 =41,274.52

Maturity date = July 9

a) What was the selling price of the note

Duration between July 9 and May 12 = 59 days

41,274.52- Selling Price = 41,274.52*27.39%*59/365

Selling Price = 39,447.12

b) What simple interest rate did the original lender earn

Interest earned = 39,447.12-40000 = -552.88

-552.88 = 40000*i*42/365

i= -12.01%

c)Simple interest rate did the company actually pay = 11.63%

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