Question

What is the price of a money market security with a discount yield of 5.38%, 145 days to maturity, and a $1000 face value? Round to $0.01.

Answer 1

Solution :

As per the Information given in the question we have

Face Value = $ 1,000   ; Current Price = To find    ; No. of days to maturity = 145

Discount yield = 5.38 % = 0.0538

The formula for calculating the discount yield is                    

Discount Yield = [ (Face value – Current Price)/ Face value ] * ( 360 / No. of days to maturity )

Applying the above values in the formula we have

0.0538 = [ ( 1000 – Current price ) / 1000 ] * ( 360/145 )

0.0538 = [ ( 1000 – Current price ) / 1000 ] * 2.482759

0.0538 / 2.482759 = ( 1000 – Current price ) / 1000

0.02166944 = ( 1000 – Current price ) / 1000

0.02166944 * 1000 = ( 10000 – Current price )

21.66944 = ( 1000 – Current price )

Current Price = 1000 – 21.66944

Current Price = 978.330556

Current Price = $ 978.330556

Current Price = $ 978.33 ( when rounded off to two decimal places )

Thus the price of a money market security with a discount yield of 5.38%, 145 days to maturity, and a $1000 face value = $ 978.33