(2) Audrey plans to retire in around 25 years. Starting from January 2023, she will make 20 years (240 months) of monthly payments made at the end of each month into her retirement saving account. Five years after her last contribution, she will begin 240 monthly withdrawals of 5,000 per month made at the beginning of each month with the first one that would be withdrew on January 1, 2048. After the negotiation with her investment agent, the retirement saving account earns interest of 4.8% p.a. compounded monthly for the whole duration including the duration of her contributions, the five years in between her contributions and the beginning of her withdrawals, and the duration of her withdrawals. (a) How much must be in Audrey's account at December 31, 2047 so that the account has sufficient funds for the subsequent withdrawals (rounding to the nearest integer)? For her monthly contributions in the first 20 years, she would contribute into the account monthly for the first 10 years. For the next 10 years, the monthly contributions would increase to 2 each. (b) Find (rounding to the nearest 1 decimal place). (c) Audrey would like to travel around the world after her retirement. She decides to include a withdrawal of 123,000 at January 1,2053 . Assuming that the amount of the regular monthly withdrawal remains to be the same, determine the date and the amount of her last withdrawal (the amount of the last withdrawal may be small than 5,000 ). For the amount, you may round your answer to the nearest integer. (2) Audrey plans to retire in around 25 years. Starting from January 2023, she will make 20 years (240 months) of monthly payments made at the end of each month into her retirement saving account. Five years after her last contribution, she will begin 240 monthly withdrawals of 5,000 per month made at the beginning of each month with the first one that would be withdrew on January 1, 2048. After the negotiation with her investment agent, the retirement saving account earns interest of 4.8% p.a. compounded monthly for the whole duration including the duration of her contributions, the five years in between her contributions and the beginning of her withdrawals, and the duration of her withdrawals. (a) How much must be in Audrey's account at December 31, 2047 so that the account has sufficient funds for the subsequent withdrawals (rounding to the nearest integer)? For her monthly contributions in the first 20 years, she would contribute into the account monthly for the first 10 years. For the next 10 years, the monthly contributions would increase to 2 each. (b) Find (rounding to the nearest 1 decimal place). (c) Audrey would like to travel around the world after her retirement. She decides to include a withdrawal of 123,000 at January 1,2053 . Assuming that the amount of the regular monthly withdrawal remains to be the same, determine the date and the amount of her last withdrawal (the amount of the last withdrawal may be small than 5,000 ). For the amount, you may round your answer to the nearest integer
