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An annuity is known as a fixed-term pension and gives a person a guaranteed income for a number of years in future. A person can use his/her savings to buy an annuity from a superannuation fund or life insurance company. We consider an annuity of a $25,000 for n = 10 years in future, and the present value of the 10-year annuity scheme is p(r) = (¹ - (,)"). wherer is the discount rate. (1) Calculate the present value p(r) when r = 1.25%. (2) Use the following first-order approximation to approximate the present value if the discount rate is increased by 0.25% (that means the discount rate is now 1.5%): p(r) p(ro) + p'(ro) x (r-ro). where r= 1.5% and ro 1.25%. Sel

An annuity is known as a fixed-term pension and gives a person a guaranteed income for a number of years in future. A person can use his/her savings to buy an annuity from a superannuation fund or life insurance company. We consider an annuity of a $25,000 for n = 10 years in future, and the present value of the 10-year annuity scheme is p(r) = (¹ - (,)"). wherer is the discount rate. (1) Calculate the present value p(r) when r = 1.25%. (2) Use the following first-order approximation to approximate the present value if the discount rate is increased by 0.25% (that means the discount rate is now 1.5%): p(r) p(ro) + p'(ro) x (r-ro). where r= 1.5% and ro 1.25%. Sel

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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An annuity is known as a fixed-term pension and gives a person a guaranteed income for a number of years in future. A person can use his/her savings to buy an annuity from a superannuation fund or life insurance company. S We consider an annuity of a $25,000 for n = 10 years in future, and the present value of the 10-year annuity scheme is p(r) = (¹ - (,)"). wherer is the discount rate. (1) Calculate the present value p(r) when r = 1.25%. (2) Use the following first-order approximation to approximate the present value if the discount rate is increased by 0.25% (that means the discount rate is now 1.5%): p(r) p(ro) + p'(ro) x (r-ro). where r= 1.5% and ro 1.25%. Sel
Transcribed Image Text:An annuity is known as a fixed-term pension and gives a person a guaranteed income for a number of years in future. A person can use his/her savings to buy an annuity from a superannuation fund or life insurance company. S We consider an annuity of a $25,000 for n = 10 years in future, and the present value of the 10-year annuity scheme is p(r) = (¹ - (,)"). wherer is the discount rate. (1) Calculate the present value p(r) when r = 1.25%. (2) Use the following first-order approximation to approximate the present value if the discount rate is increased by 0.25% (that means the discount rate is now 1.5%): p(r) p(ro) + p'(ro) x (r-ro). where r= 1.5% and ro 1.25%. Sel
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