The annuity symbol .Ia/.m/ n i gives the present value of an annuity that has payments each m-th of a year, the payments in the j -th year each being for an amount j m . That is to say, the payments are level each year and total j in the j -th year. So, the annual payments increase in arithmetic progression. Introduce a new annuity symbol .Ga/.m/ n i .r / giving the present value of an annuity that has level payments each year, the payments in the j -th year totaling .1 C r /j1 . Here the letter G stands for geometric and was chosen to reflect the fact that the underlying annuity has total annual payments that increase geometrically. Explain how you can calculate .Ga/.m/ n i .r /

(2) The annuity symbol (la) gives the present value of an annuity that has payments each m-th of a year, the payments in the j-th year each being for an amount . That is to say, the payments are level each year and total j in the j-th year. So, the annual payments increase in arithmetic progression. Introduce a new annuity symbol (Gas) giving the present value of an annuity that has level payments each year, the payments in the j-th year to- taling (1+r)-. Here the letter "G" stands for "geometric and was chosen to reflect the fact that the underlying annuity has total annual payments that increase geometrically. Explain how you can calculate (Gar). (2) The annuity symbol (la) gives the present value of an annuity that has payments each m-th of a year, the payments in the j-th year each being for an amount . That is to say, the payments are level each year and total j in the j-th year. So, the annual payments increase in arithmetic progression. Introduce a new annuity symbol (Gas) giving the present value of an annuity that has level payments each year, the payments in the j-th year to- taling (1+r)-. Here the letter "G" stands for "geometric and was chosen to reflect the fact that the underlying annuity has total annual payments that increase geometrically. Explain how you can calculate (Gar)