If parents saved $100 month in arrear for their child and he/she continues until retirement, an annual pension of approximately $32000 would have been established. If this pattern of payments started when the child reached adulthood at 21 the pension would have reached $10000 approximately.

i) Determine an expression for the accumulation of monthly payments of size Y into a fund for N years, which initially grows at an effective annual interest rate of i1 and k years after the effective annual interest rate changes to i2.

ii) Investigate the above statements and discuss your findings assuming the quoted growth of investments of 5% per annum applies permanently.

iii) Investigate further the pension statements for these two cases if growth falls to 3% per annum 40 years after the child is born. Discuss your findings