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Let j be the compound interest rate for the t-year period from time s to time s + t, and let dj be the corresponding rate of discount for that time period. Show that (a) d; = 1+j d; (b) j = - dj %3D

Let j be the compound interest rate for the t-year period from time s to time s + t, and let dj be the corresponding rate of discount for that time period. Show that (a) d; = 1+j d; (b) j = - dj %3D

Exploring Economics
Exploring Economics
8th Edition
ISBN:9781544336329
Author:Robert L. Sexton
Publisher:Robert L. Sexton
Chapter16: The Markets For Labor, Capital, And Land
Section: Chapter Questions
Problem 12P
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Use the definition of the effective rates of interest and discount.

j=[Amount at s+t - Amount at s] / [Amt at s].

d_j=[Amount at s+t - Amount at s] / [Amt at s+t].

 

For 8 items c & d, if j (d_j) is nominal then effective interest (resp. discount) every mth of a period is j^(m)/m (resp. d^(m)/m).

Let j be the compound interest rate for the t-year period from time s to time s + t, and let d; be the corresponding rate of discount for that time period. Show that j (a) d; 1+j d; () ј %3 1 - dj Show that the equivalent nominal interest and discount rates j(m) and d(m) satisfy the relationships consistent with the previous results. j(m) 1+ j(m) d(m) (с) а(m) (d) j(m) 1- d(m)
Transcribed Image Text:Let j be the compound interest rate for the t-year period from time s to time s + t, and let d; be the corresponding rate of discount for that time period. Show that j (a) d; 1+j d; () ј %3 1 - dj Show that the equivalent nominal interest and discount rates j(m) and d(m) satisfy the relationships consistent with the previous results. j(m) 1+ j(m) d(m) (с) а(m) (d) j(m) 1- d(m)
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