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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

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter8: Sequences And Series
Section8.4: Mathematics Of Finance
Problem 2E
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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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