Let us assume that the annuity purchased by the individual will pay at a rate of 8,000 per year, in equal monthly instalments paid at the beginning of each month, starting from 1st of January 2028 for 20 years. (We will refer to this annuity as retirement-annuity for the sake of clarity below.) Take i=3%

(a) Assume the individual purchases the retirement-annuity by equal quarterly payments, made at the beginning of each quarter for 10 years and starting on 1st of January 2018. What is the amount C of each payment?

(b) Assume the individual purchases the retirement-annuity by annual instalments of 5,000 at the end of each year for 10 years, plus two lump payments of equal amount L, made on 1st of January 2023 and 1st of January 2028. Compute the amount L of the lump payments.

Assume the individual has opted for quarterly payments of amount C as in (a). However, after the first payment she decides to increase the amount of contribution in order to earn a higher retirement income. Each subsequent payment increases at a rate of 1% effective per quarter. This results in a retirement-annuity rate P per annum which is larger than the original 8,000 and which will be paid from 1st January 2028.

(c) What is the new value of P ?