Question #93e58
1 Answer
This is what I get
Explanation:
Price of car
Down payment
Loan financed
For compound interest, let
#P=X/(1+r/100)^n+X/(1+r/100)^(n-1).......... +X/((1+r/100))#
Given rate of interest
Effective rate for each installment
Inserting given values we get
RHS is a GP with first term
Common ration
Sum of
#S_n=(a(r^n-1))/(r-1)#
Inserting in above expression we get
#202/3=(1/1.007(1/1.007^n-1))/(1/1.007-1)#
#202/3=((1-1/1.007^n))/(0.007)#
#=>1/1.007^n=1-202/3xx0.007#
#=>1/1.007^n=0.528bar6#
Taking log of both sides
#log(1/1.007^n)=log0.528bar6#
#-nlog1.007=log0.528bar6#
#=>n=-(log0.528bar6)/log1.007#
#=>n~~91.38=92# installments, as#n# is a positive integer, moreover installment can not be in fraction.