Question

A person invests Rs. 10,000 at 10 percent interest compounded annually. If An represents the amount at the end of n years, find a recurrence relation and initial condition that define the sequence {An}. Using the recurrence relation find amount payable after five years.

Answer 1

any person invest 10,000 Rs at the rate of 10% annually .
hence,
P = 10,000 Rs
r =10 %

according to question ,
An represents the amount at the end of n year
hence,
An =P (1 + r/100 )^n
put P and r value
An =10,000 (1 + 10/100 )^n
=10,000 ( 1 + 0.1)^n
=10,000(1.1)^n
hence,
An =10,000 (1.1)^n

put n= 1 A1=10,000 (1.1)
,, n =2 A2 =10,000 (1.1)^2
,, n =3 A3 = 10,000 (1.1)^3
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you see ,
A2/A1 = A3/A2 = (1.1)
hence, {An } geometrically increases which common ratio is (1.1)

after five year
A5=10,000 (1.1)^5
=10,000 x (1.6105)
=16105 Rs