Answer:
We get the value of Principal amount i.e initial investment = $61640
Step-by-step explanation:
Interest rate r = 3.59% or 0.0359
Compounded quarterly n = 4
Future Amount A = 117,300
Time t = 18 years
We need to find initial investment i,e Principal Amount P
The formula used is:
Putting values and finding P
So, We get the value of Principal amount i.e initial investment = $61640
Given
The formula for the sum of an infinite geometric series
used to convert 0.23 to a fraction
Find out the values of a1 and r
To proof
As given in the question
The series is infinte geometric series
The geometric is mostly in the form a , ar , ar² ,............
s = a + ar + ar² + ar³...........
Where a = first term
r = common ratio
The series is infinte geometric series i.e 0.2323...
thus it is written in the form
s = 0.23 + 0.0023 + 0.000023 +...........
now written in the fraction form
we get
compare this series with the
s = a + ar + ar² + ar³...........
Thus
we get
a1 = 0.23
r = 0.01
Hence proved