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.
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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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.
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.
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