You are borrowing $6m from the bank starting in 281 days and ending in 327 days....

You are borrowing $6m from the bank starting in 281 days and ending in 327 days. You have agreed to pay 2.50% interest on an ACT/360 basis. If interest rates are:

Days	Rates
281	2.18
327	2.94

what is the present value of this transaction? (Round your answer to the nearest 0.01)

Expert Solution

Assuming the same interest calculating convention of ACT/360

Let the fair interest rate be r for a loan starting in 281 days and ending in 327 days i.e for 46 days

The fair interest rate r should be such that an amount invested for 281 days and subsequently at r gives the same amount as amount invested for 327 days

So, exp (0.0218*281/360)* exp(r*46/360) = exp (0.0294*327/360)

=> exp (0.0218*281/360+r*46/360) = exp (0.0294*327/360)

=> (0.0218*281/360+r*46/360) = (0.0294*327/360)

=> r*46/360 + 0.017016 =0.026705

=> r*46/360 = 0.009689

=> r = 0.075826 or 7.58%

As the contracted rate is much lower than the fair rate

The value of transaction = $6 million * (7.5826%-2.5%) = $304956.52

Present value of the transaction = $304956.52* exp(-0.0294*327/360) = $296920.44

(NOTE: In case interest convention of ACT/365 is used to calculate fair value of r , it still comes as 7.58% , but since the interest rate charged is on ACT/360 basis, on ACT/360 basis, actual rate charged is 2.5347%, and the present value of transaction would be $294999.91)

jeff jeffy answered 1 year ago

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