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1 February, 12:48

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 also 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

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  1. 1 February, 12:57
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    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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