## (Solved) A borrower is given a \$ 5 0 0 , 0 0 0 3 0 year fully amortizing 3/1 Hybrid ARM with an initial rate of 2.75 % . Th e terms of the loan are as follows:...

1.A borrower is given aÂ \$500,00030Â year fullyÂ amortizingÂ 3/1Â HybridÂ ARM with an initial rate of 2.75%.Â The terms of the loan are as follows: The loan's interest rate will adjust annually according to the 10 year LIBOR index, no interest rate caps or floors, has a margin of 2%. In year 2, LIBOR is at 3.5%. In year 3, LIBOR is at 4%.Â In year 4,Â LIBOR is at 4.5%.Â How much larger (in dollars, rounded to the nearest cent) is the payment at the first reset date than the initial payment?

2.A borrower is given aÂ \$450,00030Â year fullyÂ amortizingÂ ARM with an initial rate of 5%.Â The terms of the loan are as follows: The loan's interest rate will adjust annually according to the 10 year LIBOR index, periodic cap of 2% increase , and lifetime cap of a 9% rate, has a margin of 1%. In year 2, LIBOR is at 7.5%. In year 3, LIBOR is at 5% What is the payment on this loan in year 3?

3.
A borrower is given a \$500,000Â 30Â year fully amortizingÂ ARM with an initial rate of 3.25%.Â The terms of the loan are as follows: The loan's interest rate will adjust annually according to the 10 year LIBOR index, no interest rate caps or floors, has a margin of 1.5%. In year 2, LIBOR is at 4.25%. In year 3, LIBOR is at 3.5% What is the payment on this loan in year 3?

4.Â A borrower needsÂ \$300,000Â in cash to purchase a residential property.Â The lender offers this borrower aÂ 30Â year FRM atÂ 4%Â withÂ 3Â points.Â The lender also alternatively offersÂ theÂ borrower aÂ 30Â year FRM loan forÂ \$300,000Â an no points with a rate ofÂ 4.75%?Â If the borrower plans to hold the loan forÂ 10Â years,Â what is the difference in effective interest rates between the twoÂ loans?Â (ExpressÂ yourÂ answer rounded to 2 decimal places; for example, if you answer was two and three quarters percent, enter 2.75.)

5.A borrower needsÂ \$300,000Â in cash to purchase a residential property.Â The lender offers this borrower aÂ 30Â year FRM atÂ 4%Â withÂ 3Â points.Â The lender also alternatively offersÂ theÂ borrower a 30 year FRM loan for \$300,000 an no points with a rate of 4.75%? If the borrower plans to hold the loan untilmaturity, what is the difference in effective interest rates between the two loans?Â (Express your answer rounded to 2 decimal places;

6.A borrower needsÂ \$300,000Â in cash to purchase a residential property.Â The lender offers this borrower aÂ 30Â year FRM atÂ 4%Â withÂ 3Â points.Â The lender also alternatively offersÂ theÂ borrower a 30 year FRM loan for \$300,000 an no points with a rate of 4.75%? What is the difference in required monthly payments between these two loans? (Round to the nearest cent.)

7.A borrower needs \$300,000 in cash to purchase a residential property.Â The lender offers this borrower a 30Â yearÂ FRM at 4%Â with 3Â points.Â What is the principal balance the borrower (e.g. the PV) would need to repay to the lender if he or she accepts this loan?

8.You have a loan with the following prepayment penalty schedule:

Prepay within 1 year: Penalty=5% of outstanding balanceÂ

Prepay after 1 full year butÂ before the beginning of 3rdÂ year: Penalty=4% of outstanding balanceÂ

Prepay after 2 fullÂ years but before the beginning of 4th year: Penalty=3% of outstanding balanceÂ

Prepay after 3 full years butÂ before the beginning of 5th year: Penalty=2% of outstanding balanceÂ

Prepay after 4 full years butÂ Â before the beginning of 6th yearÂ : Penalty=1% of outstanding balanceÂ

You take out a loan with this prepayment penalty schedule for \$10,000,000 to finance a commercial property. The loan is a 10 year FRM with a \$5,000,000 balloon payment, no upfront fees or points, and a 5% rate. You make regularly scheduled payments, but are thinking of prepaying the loan because market interest rates have dropped since origination. How much larger (in dollars, rounded to the nearest cent) would the prepayment penalty be if you repaid the loan after making 20 payments than if you waited until after you made 30 payments? (Hint: calculate payment on this loan, then calculate prepayment penalty under either scenario and take the difference)

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