Derivatives / Swap HELP

Does anyone know know to answer this question? Many thanks!!!

A bank has a line of credit where it can borrow funds at LIBOR + 0.20%. The bank would like to borrow funds and lend it on 30-year mortgages paying a fixed rate R. The bank requires a premium of 0.50%.

  1. Derive the formula for R if all mortgages pay interest rate only and they pay the full notional at maturity. Ignore all friction costs such as fees, tax, etc. Assume that all borrowers have no credit risk and they will make all payment to the bank.

  2. Derive the formula for R if all mortgages pay interest rate and also a part of the notional such that the notional amortizes at maturity. Ignore all friction costs such as fees, tax, etc. Assume that all borrowers have no credit risk and they will make all payment to the bank.

Anybody can help??

A bank has a line of credit where it can borrow funds at LIBOR + 0.20%. The bank would like to borrow funds and lend it on 30-year mortgages paying a fixed rate R. The bank requires a premium of 0.50%.

  1. Derive the formula for R if all mortgages pay interest rate only and they pay the full notional at maturity. Ignore all friction costs such as fees, tax, etc. Assume that all borrowers have no credit risk and they will make all payment to the bank.

Bank borrows at L+0.2% and then lends it at R = L + 0.2% + 0.5% (premium for Bank) = L+0.7%

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I am not sure how the difference between Part 1 and 2 would manifest itself on R. Possibly in case 2 - R would be between L + 0.2% and L+0.7%

That was my initial thought at first, but then how could R, a fixed rate, be determined by LIBOR, a floating rate?

that is how it is in swaps. A swap rate (Fixed) is determined in terms of the Floating rate applicable for the Floating leg - otherwise there would be arbitrage possible. In the above case - the bank could borrow at the Floating rate + 0.2% infinitely, and pay a Lower fixed rate on the mortgage - thus making money in the process, and no stopping it.