Economics Dynamics Problems 124

Economics Dynamics Problems 124 - FV = A ³(1 r n − 1 r...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
108 Economic Dynamics Example 3.7 An investor makes an initial deposit of £ 10,000 and an additional £ 250 each year. The market interest rate is 5% per annum. What are his accumulated savings after five years? For this problem, Y 0 = £ 10 , 000 , a k = £ 250 for all k and b = (1 + r ) = 1 . 05. Hence Y 5 = 250 1 (1 . 05) 5 1 1 . 05 + (1 . 05) 5 (10000) = £ 14 , 144 . 20 3.7 Discounting, present value and internal rates of return Since the future payment when interest is compounded is P t = P 0 (1 + r ) t , then it follows that the present value , PV , of an amount P t received in the future is PV = P t (1 + r ) t and r is now referred to as the discount rate . Consider an annuity. An annuity consists of a series of payments of an amount A made at constant intervals of time for n periods. Each payment receives interest from the date it is made until the end of the n th-period. The last payment receives no interest. The future value, FV , is then FV = A (1 + r ) n 1 + A (1 + r ) n 2 + · · · + (1 + r ) A + A Utilising a software package, the solution is readily found to be
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: FV = A ³ (1 + r ) n − 1 r ´ On the other hand, the present value of an annuity requires each future payment to be discounted by the appropriate discount factor. Thus the payment A received at the end of the Frst period is worth A / (1 + r ) today, while a payment A at the end of the second period is worth A / (1 + r ) 2 today. So the present value of the annuity is PV = A (1 + r ) + A (1 + r ) 2 + ··· + A (1 + r ) n − 1 + A (1 + r ) n with solution PV = A ³ 1 − (1 + r ) − n r ´ Example 3.8 £ 1,000 is deposited at the end of each year in a savings account that earns 6.5% interest compounded annually. (a) At the end of ten years, how much is the account worth? (b) What is the present value of the payments stream?...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern