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Firdavs [7]
3 years ago
11

Betty borrows 19,800 from Bank X. Betty repays the loan by making 36 equal payments of principal at the end of each month. She a

lso pays interest on the unpaid balance each month at a nominal rate of 12%, compounded monthly. Immediately after the 16th payment is made, Bank X sells the rights to future payments to Bank Y. Bank Y wishes to yield a nominal rate of 14%, compounded semi-annually, on its investment. What price does Bank X receive
Business
1 answer:
Anastaziya [24]3 years ago
5 0

Answer:

Bank X will received: $13,554.73.

Explanation:

* Calculation of Betty equal monthly repayment by using present value formula for annuity: 19,800 = PMT/1% x ( 1 - 1.01^-36) <=> PMT = $657.643

* The effective annual rate at the time of loan selling is calculated as: (1+14%/2)^2 - 1 = 14.49% => The monthly discount rate is 1.1449 ^(1/12)  -1 = 1.134%

After the 16th payment is made, there is another 20 equal repayments, made at the end of each months; so we have 20 discounting periods, PNT = 657.643; discounting rate = 1.134%

=> Price Bank X receives = Present value of the repayment stream = 657.643/0.0134 x [1 - 1.0134^(-20)] = $13,554.73.

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