April 2017 CT1 Q10

An individual aged exactly 65 intends to retire in five years’ time and receive an annuity-certain. The annuity will be payable monthly in advance and will cease after 20 years. The annuity will increase at each anniversary of the commencement of payment at the rate of 3% per annum.

The individual would like the initial level of annuity to be £20,000 per annum. The price of the annuity will be the present value of the payments on the date it commences using an interest rate of 7% per annum effective.

(i) Calculate the price of the annuity.

why is it a1 and not a20 when calculating the annuity?

 

Within each year it is as the amount is payable monthly in advance. This brings value of all 12 monthly payments made during each year to the beginning of that year. However, this happens every year for 20 years with an increase of 3% at each anniversary. This value is reflected by multiplying with G.P series ( 1+1.03V+...............20 years in total). Attached timeline

 

thank you very much! makes sense now