Unformatted text preview: x and ln x , respectivelyâ€”the latter being described as a natural logarithms or Naperian logarithms. 5. Let S n = 1 + r + r 2 + Â· Â· Â· + r n âˆ’ 1 , which is a partial sum of n terms of an geometric progression. Show that S n + r n = 1 + rS n and thence derive an expression of S n in terms of r . 6. Annual payments of Â£ M must be made over a period of n years to redeem a mortgage. The present value of this stream of payments is M ( Î´ + Î´ 2 + Â· Â· Â· + Î´ n ) , where Î´ = (1 + r ) âˆ’ 1 is the rate of discount and r is the rate of interest. The present value of the stream of payments must equate to the value L of the loan. If the loan was for Â£ 150,000 and the rate of interest was Â±xed a 5% for the entire period, what should be the size of the annual payment in order to redeem the loan in 20 yearâ€™s time? 1...
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This note was uploaded on 03/02/2012 for the course EC 3070 taught by Professor D.s.g.pollock during the Spring '12 term at Queen Mary, University of London.
- Spring '12