Calculate the nominal rate of interest per annum convertible half-yearly that is equivalent to: (i) (iii) an effective rate of discount of 0.5% per month a nominal rate of discount of 6% per annum convertible every 2 years a nominal rate of interest of 6% per annum convertible quarterly

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Please explain  calculation of transaction b)  Where the value 612 is coming

PLEASE, WRITE THE SOLUTIONS ON PAPER, EXPLAINING THE ENTIRE PROCESS, THE ONLY AND CORRECT ANSWERS ARE FOR (i) V(t) = exp (-2e^0.02t + 2 ) for 0 15 (i) Derive, and simplify as far as possible, expressions in terms of t for V(t), where V(t) is the present value of a unit sum of cash flow made at time t. You should derive separate expressions for the three sub-intervals. (ii) Hence, making use of the result in part (i), calculate the value at time t = 3 of a payment of £2,500 made at time t = 15. (iii) Calculate, to the nearest 0.01%, the constant nominal annual rate of interest convertible half-yearly implied by the transaction in part (ii). (iv) Making use of the result in part (i), calculate the present value of a payment stream p(t) paid continuously from time t = 15 to t = 20 at a rate of payment at time t given by: p(t) = 300e 0.02t