A local store sells a 60″ Full HD plasma TV for $30 per week to be paid in 25 months. If the cash value is $1, 870 find the approximate effective interest rate per year charged on this purchase. 0% 26% 52% 33% 78%

A local store sells a 60″ Full HD plasma TV for $30 per week to be paid in 25 months. If the cash value is $1, 870 find the approximate effective interest rate per year charged on this purchase. 0% 26% 52% 33% 78%

 

answer:

where

E is Weekly payment = $30

P is Principal Loan Amount = $1870

r is rate of interest calculated on weekly basis. (i.e., r = Rate of Annual interest/12/4/100. If rate of interest is 10.5% per Year, then r = 10.5/12/4/100)

n is loan term / tenure / duration in number of Weeks = 24*4 = 96 weeks

So,

$30 = $1870*r*(1+r)^96/[(1+r)^96 – 1]

(1+r)^96 – 1 = 62.33*r*(1+r)^96

(1+r)^96[1 – 62.33*r] = 1

Taking log on both sides

96log(1+r) + log[1-62.33*r] = log1

Solving for r by taking the anti log

So, r = 52%

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