Respuesta :
Answer:
1) Function of option [tex],A=5000(1.045)^t[/tex]
option [tex]B =5000(1.0115)^(4t)[/tex].
2)After 6 years, how much more money option B will earn than option A is 67.57 $.
3)It would take 15 years for option B to double Seth’s initial investment.
Step-by-step explanation:
Given:
Initial Investment=5000$
Option A(rate)= 4.5% .....annually
Option B(rate)=4.6 %..........Quarterly
To Find:
1)Write a function of option A and option B
2)After 6 years, how much more money option B will earn than option A
3) how long it would take for option B to double Seth’s initial investment.
Solution:
To write the function use formula of compound interest as ,
[tex]A=P(1+r)^t[/tex]
For option A ,P=5000$ r=4.5 % annually
[tex]A=5000(1+0.045)^t[/tex]
[tex]A=5000(1.045)^t[/tex]
For Option B ,P=5000$ r=4.6 % Quarterly
[tex]B=5000(1+0.046/4)^(4t)[/tex]
[tex]B=5000(1+0.0115)^(4t)[/tex]
[tex]B=5000(1.0115)^(4t)[/tex]
2)After 6 years, how much more money option B will earn than option A,
Here t=6 so Above equation will be ,
[tex]A=5000(1.045)^t[/tex]
[tex]A=5000(1.045)^6[/tex]
[tex]A=6511.30 $[/tex] $
For Option B
B=5000(1.0115)^ 4*6
[tex]B=5000(1.0115)^(24)[/tex]
[tex]B=6578.87[/tex] $
B will earn more money as
therefore B -A
[tex]=6578.67 -6511.30[/tex]
=67.57 $
3)how long it would take for option B to double Seth’s initial investment
By doubling the invest i.e for 10000 $ how much time will required.
So B=10000$ , P=5000$ and r= 4.5 % Quarterly
10000=5000(1.0115)^4t
2=(1.0115)^4t
Using the definition of the logarithm as ,
4t=Log2 with base 1.0115............. use this in calculator
4t=60.62
t=15.155 years
i.e, t=15 years.
