Question

Mark signs a note promising to pay $300 in 2.5 years with simple interest at 9.75%. Then, 12 months before the note comes due, the holder of the note sells it to a local bank which discounts the note based on a bank discount rate of 17%.

(a) What did the bank pay the holder of the note when it was sold 12 months before maturity?

(b) What simple interest rate did the holder of the note earn for the time the note was held? (Enter your answer as a percent. If your answer is less than 0, type 9999)

Answer 1

Solution:-

(a)

Mark has promised to pay $300 after 2.5 years alongwith simple interest at 9.75% per annum.

Total interest payable for 2.5 years= ($300*9.75%)*2.5= $73.125

Thus, Mark will pay a total of $373.125 at the end of 2.5 years against the promissory note. When the holder takes it to the bank at the end of 1.5 years, the bank would discount the said receivable sum of $373.125 at the rate of 17% and pay the holder as follows:

Amount bank paid to holder= $373.125/(1+17%)= $318.91

This way the bank would make a 17% return on the said transaction which is the discount rate as well.

(b)

Total interest earned by holder for 1.5 years = ($318.91-$300)= $18.91

Annual simple interest for $18.91 made for 1.5 years period= ($18.91/$300)*(1/1.5)= 4.2%