You have just purchased a four-month, $600,000 negotiable CD, which will pay a 7.5 percent annual...

You have just purchased a four-month, $600,000 negotiable CD, which will pay a 7.5 percent annual interest rate.

a. If the market rate on the CD rises to 8 percent, what is its current market value?
b. If the market rate on the CD falls to 7.25 percent, what is its current market value?

Expert Solution

The payout of the four-month $600000 negotiable CD at 7.5% annual interest rate is calculated as:
=$600000*(1+7.5%*4/12)
Here 4 refers to the time period of the CD, that is 4 months and 12 refers to the total months in the year.
Payout=$600000*(1+7.5%*4/12)
=$600000*(1.025)
=$615000

Part a:
Here, we need to calculate the amount that pays $615000 (in 4 months time) when invested at 8%.
So, amount*(1+8%*4/12)=$615000
Here, 4 refers to the time period in months and 12 refers to the total months in the year.
=>Amount*(1+8%*4/12)=$615000
=>Amount*(1.026666667)=$615000
=>Amount=$615000/(1.026666667)=$599025.9738

So, current value=$599025.9738

Part b:
Here, we need to calculate the amount that pays $615000 (in 4 months time) when invested at 7.25%.
So, amount*(1+7.25%*4/12)=$615000
Here, 4 refers to the time period in months and 12 refers to the total months in the year.
=>Amount*(1+7.25%*4/12)=$615000
=>Amount*(1.024166667)=$615000
=>Amount=$615000/(1.024166667)=$600488.2016

So, current value=$600488.2016

jeff jeffy answered 1 year ago

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