Solve 6-Month CD Yield Problem for Bank: USD 3M at 3.50% p.a.

[Andersxman]

Homework Statement

Assume that a bank wanted to issue a CD with a total face amount of USD 3,000,000 for 6 months (181 days). The coupon rate that the bank wanted to pay was 3.50% p.a.

Currently the market is only demanding a 3.25% p.a. yield on a money market basis for 6-month CDs issued by comparable (credit rating and name recognition) banks. What is the price of the CD that the bank can issue? Input your answer correct to two decimal places.

Anyone able to help me with a method for calculating this?



So my confusion has everything to do with "P" - I am trying to find out what P is, and I need P to do that(?)

Anyone?

Homework Equations

Apparantly, the "formula" is something like this:

Y = (R/I -1) * 360/d

Y = annualized yield of the investment on a money market basis
R = Proceeds from the investment
I = initial investment amount (But this is what I don't get - in my material it is stated that the I is "initial investment amount * P", and P is the price.. Also, P is the solution to the question..

The Attempt at a Solution

Y = 3000000 X (1+(0.035*(181/360)) = 3.052.791,667

3.052.791,667 / 3000000 = 1,017597222
1,017597222 - 1 = 0,017597222
0,017597222 X (360/181) = 0,035


The problem is that "I" (the initial investment amount) in this formula needs to be the amount that will make the CD yield exactly 3,25%.

The answer must be that the CD will be sold for more than the 3000000, but I cannot figure out how much more.. Anyone?

I would really appreciate some help on this, I have been staring at it for a while.

 

[mighty2000]

Thanks!

Hi there,

To calculate the price of the CD, you can use the following formula:

P = F/(1+Y*d/360)

Where:
P = price of the CD
F = face amount of the CD (in this case, $3,000,000)
Y = annualized yield on a money market basis (in this case, 3.25%)
d = number of days in the term (in this case, 181)

So, in this case, P = 3000000/(1+0.0325*181/360) = $2,961,165.05

This means that the bank can issue the CD for $2,961,165.05 in order to pay a coupon rate of 3.50% and still achieve a yield of 3.25% on a money market basis. This is because the market is currently only demanding a 3.25% yield, so the bank can issue the CD at a lower price and still attract investors.

I hope this helps! Let me know if you have any other questions.