To expand his business, Happy took a loan of $1million from a bank on 1 January 2020 which he will need to completely payoff by 31 December 2034. The bank will charge interest as follows. • 5% per...

Extracted text: To expand his business, Happy took a loan of $1million from a bank on 1 January 2020 which he will need to completely payoff by 31 December 2034. The bank will charge interest as follows. • 5% per annum effective for the first 5 years, • 4% per quarter-year effective for the next 5 years, and • 1% per month effective thereafter. Happy will make repayments in dollars to the bank as follows. No repayments to be made in the first 5 years. • In calendar years 2025-2029 he will make quarterly repayments. The repayments in 2025 will be Y per quarter, and in each subsequent year the repayments will increase by 10% meaning that in 2026 the repayments will be 1.1Y per quarter and so on utill in year 2029 the quarterly repayments will be 1.14Y. In calendar years 2030-2034 he will make monthly repayments. The repayments in 2030 will be 0.5Y per month, and in each subsequent year the repayments will increase by 5% meaning that in 2031 the repayments will be 1.05(0.5Y) per month and so on utill in year 2034 the monthly repayments will be 1.05 (0.5Y). Show that the value on 1 January 2030 of the repayments made in the calendar years 2030-2034 is 24.5537Y. (a) Show that the value on 1 January 2025 of the repayments made in the calendar years 2025-2029 is 16.1075Y. (b) (c) Hence, calculate the value of Y to the nearest integer.