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A bank has made a three-year $10 million dollar loan that pays annual interest of 8 percent
A bank has made a three-year $10 million dollar loan that pays annual interest of 8 percent. The principal is due at the end of the third year.
a. The bank is willing to sell this loan with recourse at an interest rate 8.5 percent? What price should it receive for this loan?
b. The bank has the option to sell this loan without recourse at a discount rate of 8.75 percent. What price should it receive for this loan?
Expert Solution
a). Computation of the price of the loan:-
Coupon payment = $10,000,000*8% = $800,000
Price of the loan = C*((1-1/(1+r)^n)/r) + (FV/(1+r)^n)
= 800000*((1-1/(1+8.5%)^3)/8.5%) + (10000000/(1+8.5%)^3)
= (800000 * 2.5540) + (10000000/1.2773)
= $2,043,217.90 + $7,829,080.98
= $9,872,298.88 Or $9.8723 million
b). Computation of the price of the loan:-
Coupon payment = $10,000,000*8% = $800,000
Price of the loan = C*((1-1/(1+r)^n)/r) + (FV/(1+r)^n)
= 800000*((1-1/(1+8.75%)^3)/8.75%) + (10000000/(1+8.75%)^3)
= (800000*2.5426) + (10000000/1.2861)
= $2,034,092.48 + $7,775,211.35
= $9,809,303.83 Or $9.8093 million
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