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Ne4ueva [31]
3 years ago
15

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.
Mathematics
1 answer:
umka21 [38]3 years ago
5 0

Answer:

1) Function of option ,A=5000(1.045)^t

option B =5000(1.0115)^(4t).

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 ,

A=P(1+r)^t

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

A=5000(1+0.045)^t

A=5000(1.045)^t

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

B=5000(1+0.046/4)^(4t)

B=5000(1+0.0115)^(4t)

B=5000(1.0115)^(4t)

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

Here t=6 so Above equation will be ,

A=5000(1.045)^t

A=5000(1.045)^6

A=6511.30 $ $

For Option B

B=5000(1.0115)^ 4*6

B=5000(1.0115)^(24)

B=6578.87 $

B will earn more money as

<em>therefore </em> B -A

=6578.67 -6511.30

=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..........<em>... </em><em>use this in calculator</em>

4t=60.62

t=15.155 years

i.e, t=15 years.

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