In this workout, we're told a certificate of deposit has been issued with a coupon of 5.5%. The original term was for six months, starting on the 15th of January 2060. But a client is looking to sell the CD in the secondary market, assuming there are 30 days left to maturity, calculate the current price of the CD using the yield curve data given below. So here's our yield curve data. We're given some yields for 30 days, three months and six months. We'll come back to that. The current coupon rate given in the question 5.5% there it is, and we started our investment on the 15th of January, and we're finishing on the 15th of July. That's 182 Interest rate days. Days left in maturity is 30, and the day count convention we'll use is 360. So we need to do two things here. We firstly need to work out what the future value of the CD would be at the end of the six months, but we're not selling it then. We're selling it 30 days early. So once we've got that future value, we'll then discount that by 30 days.

So let's calculate that future value of the CD. Well, we bought it for 100% value, but we now need to grow it by 1 plus the coupon rates, that coupon rates was 5.5%.

However, that 5.5% is for a whole year of coupon. We're only getting six months worth of coupon. So I'm going to multiply that by the 182 divided by 360. So that will give us six months worth of coupon. So the future value of the CD goes up from a 100% to 102.781%. Great, but that's not its value now, that's its value at the end of the six months, we need to discount that by 30 days. So my present value, I'll take that future value and I'll divide it by 1 plus. And now I need the 30 day yield rate, go up to the yields curve data, and the 30 day figure is 5.540%. That's for a whole year. I only need to discount it by 30 days. So I'll multiply that by 30 over 360, close the brackets. Great. I've discounted the 102.781% back to today to get a new price of 102.308% of face value.