A publication about pensions stated that if parents were to save 100 per month in arrear...

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A publication about pensions stated that if parents were to save £100 per month in arrear for their child and the child continues the payments when in employment until retirement, an annual pension of approximately £32,000 would have been established. The same article reported that if this pattern of payments started when the child reached adulthood at 21 the pension would have reached approximately £10,000. 1. 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 in and after k years the effective annual interest rate changes to iz. (i) Investigate the above statements and discuss your findings assuming that a quoted growth of investment of 5% per annum applies permanently. (ii) Investigate further the pension statements for these two cases if the growth falls to 3% per annum 40 years after the child is born. Discuss your results. You may assume that the retirement age is 67. State clearly any other assumptions you make. In your calculations and discussions, comment on the duration of the pension. A publication about pensions stated that if parents were to save £100 per month in arrear for their child and the child continues the payments when in employment until retirement, an annual pension of approximately £32,000 would have been established. The same article reported that if this pattern of payments started when the child reached adulthood at 21 the pension would have reached approximately £10,000. 1. 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 in and after k years the effective annual interest rate changes to iz. (i) Investigate the above statements and discuss your findings assuming that a quoted growth of investment of 5% per annum applies permanently. (ii) Investigate further the pension statements for these two cases if the growth falls to 3% per annum 40 years after the child is born. Discuss your results. You may assume that the retirement age is 67. State clearly any other assumptions you make. In your calculations and discussions, comment on the duration of the pension.

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ANSWER Let Y be the monthly payment N be the number of years i1 be the initial effective annual inte... View the full answer