An individual deposits £10,500 each year into a tax-free savings plan over a 20-year period. The payments are made monthly in arrears during the first 5 years and thereafter quarterly in arrears for the remaining 15 years. The savings plan pays compound interest at the rates of: (i) 6% p.a. nominal convertible monthly for the first 10 years, and 7.5% p.a. nominal convertible quarterly for the remaining 10 years. Calculate the total amount of fund accumulated in the savings plan at the end of the 20- year period. (ii) At the end of the 20-year period, the individual intends to invest the total savings into a level fixed term annuity product that provides a future retirement income. Calculate the monthly income that the individual can obtain by investing the sum calculated in part (i) into a 25-year term annuity payable monthly in arrears at an effective interest rate of 4.5% p.a.
An individual deposits £10,500 each year into a tax-free savings plan over a 20-year period. The payments are made monthly in arrears during the first 5 years and thereafter quarterly in arrears for the remaining 15 years. The savings plan pays compound interest at the rates of: (i) 6% p.a. nominal convertible monthly for the first 10 years, and 7.5% p.a. nominal convertible quarterly for the remaining 10 years. Calculate the total amount of fund accumulated in the savings plan at the end of the 20- year period. (ii) At the end of the 20-year period, the individual intends to invest the total savings into a level fixed term annuity product that provides a future retirement income. Calculate the monthly income that the individual can obtain by investing the sum calculated in part (i) into a 25-year term annuity payable monthly in arrears at an effective interest rate of 4.5% p.a.
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:An individual deposits £10,500 each year into a tax-free savings plan over a 20-year period. The
payments are made monthly in arrears during the first 5 years and thereafter quarterly in arrears for
the remaining 15 years.
The savings plan pays compound interest at the rates of:
●
●
(i)
6% p.a. nominal convertible monthly for the first 10 years, and
7.5% p.a. nominal convertible quarterly for the remaining 10 years.
Calculate the total amount of fund accumulated in the savings plan at the end of the 20-
year period.
(ii) At the end of the 20-year period, the individual intends to invest the total savings into a
level fixed term annuity product that provides a future retirement income. Calculate the
monthly income that the individual can obtain by investing the sum calculated in part (i)
into a 25-year term annuity payable monthly in arrears at an effective interest rate of
4.5% p.a.
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correct answers:
(i) A20 = £455,154.48
(ii) R = £2,506.64 pm
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