(i) Consider an n-year increasing annuity payable annually in arrears, where the rate of payment at the end of the first year is £1, the payment at the end of the second year is £2, and so on until the final payment at the end of year n is of amount £n. Show that the present value of this annuity is given by: ἅπι – ηνη (la) | = - i (ii) A loan is repayable by decreasing quarterly instalments made in arrears for 8 years. The payment made at the end of the first quarter year is £2,100 and subsequent payments decrease by £20 each quarter. The instalments were calculated using a nominal rate of interest of 6% per annum convertible quarterly. (a) Calculate the original amount of the loan in whole pounds. (b) Calculate the amount of interest and capital components in the 10th instalment. (c) Immediately after the 10th instalment has been made, it is agreed that the annual decrease will no longer occur. Thus, the future instalments will continue at the same level as in the 10th payment, for a shorter term, and with a smaller amended payment at the end of the loan contract. 1. 2. Calculate the remaining revised term of the loan in whole quarter years. Calculate, to 2 decimal places, the amount of the final amended instalment.
(i) Consider an n-year increasing annuity payable annually in arrears, where the rate of payment at the end of the first year is £1, the payment at the end of the second year is £2, and so on until the final payment at the end of year n is of amount £n. Show that the present value of this annuity is given by: ἅπι – ηνη (la) | = - i (ii) A loan is repayable by decreasing quarterly instalments made in arrears for 8 years. The payment made at the end of the first quarter year is £2,100 and subsequent payments decrease by £20 each quarter. The instalments were calculated using a nominal rate of interest of 6% per annum convertible quarterly. (a) Calculate the original amount of the loan in whole pounds. (b) Calculate the amount of interest and capital components in the 10th instalment. (c) Immediately after the 10th instalment has been made, it is agreed that the annual decrease will no longer occur. Thus, the future instalments will continue at the same level as in the 10th payment, for a shorter term, and with a smaller amended payment at the end of the loan contract. 1. 2. Calculate the remaining revised term of the loan in whole quarter years. Calculate, to 2 decimal places, the amount of the final amended instalment.
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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Just do part I)
Transcribed Image Text:(i) Consider an n-year increasing annuity payable annually in arrears, where the rate of
payment at the end of the first year is £1, the payment at the end of the second year
is £2, and so on until the final payment at the end of year n is of amount £n. Show
that the present value of this annuity is given by:
ἅπι – ηνη
(la) | =
-
i
(ii) A loan is repayable by decreasing quarterly instalments made in arrears for 8 years.
The payment made at the end of the first quarter year is £2,100 and subsequent
payments decrease by £20 each quarter. The instalments were calculated using a
nominal rate of interest of 6% per annum convertible quarterly.
(a) Calculate the original amount of the loan in whole pounds.
(b) Calculate the amount of interest and capital components in the 10th instalment.
(c) Immediately after the 10th instalment has been made, it is agreed that the
annual decrease will no longer occur. Thus, the future instalments will continue
at the same level as in the 10th payment, for a shorter term, and with a smaller
amended payment at the end of the loan contract.
1.
2.
Calculate the remaining revised term of the loan in whole quarter years.
Calculate, to 2 decimal places, the amount of the final amended
instalment.
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