Question

The annualized discount rate on a particular money market instrument, is 4.25%. The face value is $100,000, and it matures in 45 days. What is its price? What would be the price if it had 62 days to maturity?

Answer 1

I have answered the question below

Please up vote for the same and thanks!!!

Do reach out in the comments for any queries

Answer:

The price with 45 days maturity is calculated as follows:

Annualized Discount Rate = [(Face Value - Price of Money Market Instrument)/Face Value]*360/Maturity Period

Substituting the values provided in the question, we get,

4.25% = [(100,000 - Price of Money Market Instrument)/100,000]*360/45

Rearranging Values, we get,

4.25%*45/360*100,000 = 100,000 - Price of Money Market Instrument

Price of Money Market Instrument = 100,000 - 531.25 = $99468.75

The price with 62 days maturity is calculated as follows:

Annualized Discount Rate = [(Face Value - Price of Money Market Instrument)/Face Value]*360/Maturity Period

Substituting the values provided in the question, we get,

4.25% = [(100,000 - Price of Money Market Instrument)/100,000]*360/62

Rearranging Values, we get,

=> 4.25%*62/360*100,000 = 100,000 - Price of Money Market Instrument

Price of Money Market Instrument = 100,000 - 731.9444 = $99268.06