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23. A bank is in the process of renegotiating a three-year nonamortizing loan. The principaloutstanding is $20 million, and the interest rate is 8 percent.

23. A bank is in the process of renegotiating a three-year nonamortizing loan. The principaloutstanding is $20 million, and the interest rate is 8 percent. The new terms will extend theloan to 10 years at a new interest rate of 6 percent. The cost of funds for the bank is 7 percentfor both the old loan and the renegotiated loan. An up-front fee of 50 basis points is to beincluded for the renegotiated loan.

a. What is the present value of the existing loan for the bank?

PV of old loan =PVAn=3,k=7%($1.6m) + PVn=3,k=7%($20m) = $20.5249 million

Can someone please explain how they got the Present Value in the above answer for the question? Why is there a PVA and a PV - and why are they using 7%?

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