Q3. (a) (s MARKS] Consider an annuity with n = n1 + n2 payment periods. Let i be the interest rate per conversion period. Let R, be the amount of each of the first ni periodic payments and R, be the amount of each of the remaining lic payments. Let A denote the present value of such an annuity. Show that A= Rami + R20 (1 + i)". na pe (b) (5 MARKS] Use part (a) to show that the present value of a deferred annuity is Adet = Rami(1+i)* where k is the number of deferred payments, R is the amount of the pay- ments and n is the number of payments. Give a formula for the future value of a deferred annuity at time k +n interest conversion periods. 1 TIT from 9500 dour and 24 monthly payments of Q3. (a) (s MARKS] Consider an annuity with n = n1 + n2 payment periods. Let i be the interest rate per conversion period. Let R, be the amount of each of the first ni periodic payments and R, be the amount of each of the remaining lic payments. Let A denote the present value of such an annuity. Show that A= Rami + R20 (1 + i)". na pe (b) (5 MARKS] Use part (a) to show that the present value of a deferred annuity is Adet = Rami(1+i)* where k is the number of deferred payments, R is the amount of the pay- ments and n is the number of payments. Give a formula for the future value of a deferred annuity at time k +n interest conversion periods. 1 TIT from 9500 dour and 24 monthly payments of