plz answer all parts

Part 1: Assume a constant force of interest throughout. (a) An n year annuity payable p-thly in arrear is expressed as an](p)=i(p)1vn=i(p)ian] where i(p) is the nominal rate of interest per unit time, payable p-thly, i is the effective rate of interest per unit time and v is the present value of 1 due at time 1 . (b) Show the second equality in (1) (i.e. the left hand side is equal to the right hand of the second equality). (c) On the basis of an effective rate of interest of 10% per annum, find the present value of an annuity of 450 per annum, for 15 years, payable i Annually in arrears, ii Monthly in arrears, iii Quarterly in arrears. You may work in units of 1 year and express your answers to the nearest pound. (d) Following along the lines shown in lectures, take the limit of (1) as n. For what effective rate of interest i is this valid