Prob Set 33 AE Please assist on E if possible 3 35 points As

Prob Set 3.3 (A-E), Please assist on E if possible

3. (3.5 points) Assume a bank issues a 30-year fixed-rate $250,000 mortgage at 4.25% and keeps that mortgage in its loan portfolio.

a. Calculate and report the monthly payments for the mortgage.  

b. Assume that immediately after it is issued, the bank wants to sell its mortgage, but interest rates have risen to 6.25%. At what price would the bank be able to sell its mortgage?

c. Assume that immediately after it is issued, the bank wants to sell its mortgage, but interest rates have risen to 7.75%. At what price would the bank be able to sell its mortgage?

d. Assume that immediately after it is issued, the bank wants to sell its mortgage, but interest rates have fallen to 3.25%. At what price would the bank be able to sell its mortgage?

e. Explain in a full essay why the bank might have trouble selling the mortgage at the price you calculated in part d, when rates have fallen to 3.25%?

Solution

a. Monthly payment for mortgage:

EMI = Principal/Present value interest factor.

=250000/(1-1/(1+r)^n)/r

now, r = 4.25%/12, n = 30*12

=250000/(1-(1/(1+(4.25%/12))^360))/(4.25%/12)

=1229.85

b. when interest rate rise to 6.25%

the bank will be able to sell it for 6.25%, since the bank has issued it on 4.25%, bank is still making a profitabe deal.

c. when interest rate rise to 7.75%

the bank will be able to sell it for 7.75%, since the bank has issued it on 4.25%, bank is still making a profitabe deal.

d. when interest rate rise to 3.25%

the bank will be able to sell it for 4.25%, since the bank has issued it on 4.25%, and selling it at 3.25% will be a loosing deal

e. since the bank has issued the mortgage at 4.25% and bank may make loss if selling the same at 3.25% which will lead bank at loss of 1%. since the bank is already paying the interest of 4.25%, the bank will never be ready to receive less interest then paying.

pls let me know if any queries