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

a) Total interest payable after 2.5 years = $300 * 9.75% * 2.5 = $73.125

Total amount to be payed by Mark at the end of 2.5 years = $300 + 73.125 = $373.125.

When the holder takes it to the bank at the end of 1.5 years, the bank would discount the amount of $373.125 @ 17% and pay the holder = 373.125 / (1+0.17) = $318.91.

Hence the bank would pay $318.91 to the holder.

b) Interest earned by holder for 1.5 years = 318.91 - 300 = $18.91.

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

Hence the holder earned an annual rate of 4.2% on the note.

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