Answer:
a.The total amount that Molly will have in her account at the end of 3 years is $345.60
b. The sum of finite G.P series , @@MATH_TOKEN_0@@when r<1
The sum of finite G.P series ,@@MATH_TOKEN_1@@ when r>1
Step-by-step explanation:
Given
Molly deposits saving in her account= $200
Interest rate=20%
Time =3 years
Amount,A\(=P(1+\frac{r}{100})^t\)
Where P= principle value
r= Interest rate annually
t= time in years
A=Amount
P=$200
r=20%
t=3 years
Substitute all values in the given formula
A=@@MATH_TOKEN_3@@
A=@@MATH_TOKEN_4@@
A=@@MATH_TOKEN_5@@
A=@@MATH_TOKEN_6@@
A=345.6
Amount=$345.6
Hence, Molly will have total amount in her account at the end of 3 years is $345.6.
b. Let finite G. P series
\(a,ar,ar^2,ar^3,..........ar^{n-1}\)
Total terms=n
\(a_1=a,a_2=ar,a_3=ar^3\)
\(\frac{a_2}{a_1}=\frac{ar}{a}=r\)
\(\frac{a_3}{a_2}=\frac{ar^2}{ar}=r\)
Hence, common ratio=r
Sum of finite G.P series,\(S_n=\frac{a(r^n-1)}{r-1}\) when r>1
Sum of finite G.P series,\(S_n=\frac{a(1-r^n)}{1-r}\) when r<1.
