(a) Write down an equation of value for each savings plan and hence use linear interpolation to find the yield for each. (b) Assume that an investor opts for plan (i) and that after three years he investsthe proceeds of the plan for a further two years at a fixed rate of interest. How large must this rate of interest be in order for him to receive $1550 from this investment? (c) Assume that the investor opts for plan (ii) and that after five years he uses theproceeds of the plan to buy a level annuity payment for 4 years being calculated on the basis of a fixed interest rate. How large must this interest rate be in order for the annuity payment to be $425?

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Q1. In return for a single payment of $1000, a building society offers the following alternative
benefits:
(i) A lump sum of $1330 after 3 years;
(ii) A lump sum of $1550 after five years; or
(ii) Four annual payments, each of amount $425, the first payment being made after
five years.
Any investor must specify which benefit he is choosing when he makes the single
рayment.
(a) Write down an equation of value for each savings plan and hence use linear
interpolation to find the yield for each.
(b) Assume that an investor opts for plan (i) and that after three years he investsthe
proceeds of the plan for a further two years at a fixed rate of interest. How large
must this rate of interest be in order for him to receive $1550 from this
investment?
(c) Assume that the investor opts for plan (ii) and that after five years he uses
theproceeds of the plan to buy a level annuity payment for 4 years being
calculated on the basis of a fixed interest rate. How large must this interest rate
be in order for the annuity payment to be $425?
Transcribed Image Text:Q1. In return for a single payment of $1000, a building society offers the following alternative benefits: (i) A lump sum of $1330 after 3 years; (ii) A lump sum of $1550 after five years; or (ii) Four annual payments, each of amount $425, the first payment being made after five years. Any investor must specify which benefit he is choosing when he makes the single рayment. (a) Write down an equation of value for each savings plan and hence use linear interpolation to find the yield for each. (b) Assume that an investor opts for plan (i) and that after three years he investsthe proceeds of the plan for a further two years at a fixed rate of interest. How large must this rate of interest be in order for him to receive $1550 from this investment? (c) Assume that the investor opts for plan (ii) and that after five years he uses theproceeds of the plan to buy a level annuity payment for 4 years being calculated on the basis of a fixed interest rate. How large must this interest rate be in order for the annuity payment to be $425?
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