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. Show that the value on 1 January 2025 of the repayments made in the calendar years 2025-2029 is 16.1075Y. Hence, calculate the value of Y to the nearest integer.
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. Show that the value on 1 January 2025 of the repayments made in the calendar years 2025-2029 is 16.1075Y. Hence, calculate the value of Y to the nearest integer.
Chapter5: Introduction To Business Expenses
Section: Chapter Questions
Problem 61P
Related questions
Question
Transcribed Image 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.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 8 images
Recommended textbooks for you
Principles of Accounting Volume 1
Accounting
ISBN:
9781947172685
Author:
OpenStax
Publisher:
OpenStax College
EBK CONTEMPORARY FINANCIAL MANAGEMENT
Finance
ISBN:
9781337514835
Author:
MOYER
Publisher:
CENGAGE LEARNING - CONSIGNMENT
Principles of Accounting Volume 1
Accounting
ISBN:
9781947172685
Author:
OpenStax
Publisher:
OpenStax College
EBK CONTEMPORARY FINANCIAL MANAGEMENT
Finance
ISBN:
9781337514835
Author:
MOYER
Publisher:
CENGAGE LEARNING - CONSIGNMENT