Seth’s parents gave him $5000 to invest for his 16th birthday. He is considering two investment options. Option A will pay him 4.5% interest compounded annually. Option B will pay him 4.6% compounded quarterly. 1) Write a function of option A and option B that calculates the value of each account after n years. 2) Seth plans to use the money after he graduates from college in 6 years. Determine how much more money option B will earn than option A to the nearest cent. 3) Algebraically determine, to the nearest tenth of a year, how long it would take for option B to double Seth’s initial investment.

1) Function of option

option .

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 ,

For option A ,P=5000$ r=4.5 % annually

For Option B ,P=5000$ r=4.6 % Quarterly

2)After 6 years, how much more money option B will earn than option A,

Here t=6 so Above equation will be ,

$

For Option B

B=5000(1.0115)^ 4*6

$

B will earn more money as

therefore B -A

=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.

not enough information

step-by-step explanation:

we cannot know this, because the other students could have handed out 10 flyers, or they could have handed out 100. one way, the mean would go up, and another way, the mean would go down.

i think it would be 42cm