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) dj = i dj (b) j = 1- dj 1+ j Show that the equivalent nominal interest and discount rates j(m) and dm) satisfy the relationships consistent with the previous results. c) d(m) = d) į(m) d(m) %3D ms 9, pdf (m) 1+ = (u)? 1- (u)P 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) dj = i dj (b) j = 1- dj 1+ j Show that the equivalent nominal interest and discount rates j(m) and dm) satisfy the relationships consistent with the previous results. c) d(m) = d) į(m) d(m) %3D ms 9, pdf (m) 1+ = (u)? 1- (u)P m
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
ONLY ANSWER C & D
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 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).
Note: 2nd photo is my answer & solution for items a & b
Transcribed Image Text:d
d be discout rate
+j
tet
Altt= A(z)- dAlz)
Al1) = A(2){!-d).
itj
Alo)2A(1)-Ali)d
to
fatring
Alo) = Alo) (I-d)"
Primciplealu (Presint valu
I+j.
d = }
Itj
valur
it'j
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In Genueef
P= Alt) (-d)t
(1) by mamupulating aboue Kelautia
%3D
Alt)-
Intenast comnted campeundily
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1५ च्य
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) dj
1+ j
d;
(b) j =
1 – dj
%3D
|
Show that the equivalent nominal interest and discount rates j(m) and d'm) satisfy the relationships
consistent with the previous results.
c)
d(m) =
d)
(m) =
{(m)
d(m)
į (m)
1+
(1)P
m
ms 9,
pdf
1
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