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Answer:
Part A: The value of the simple interest investment at the end of three years is $12,220
Part B: The value of the compounded quarterly interest investment at the end of three years is $12,134.08
Part C: The simple interest investment is better over the first three years
Part D: I advise George to invest his money in the compounded interest investment if he will keep the money for a long time
Step-by-step explanation:
Part A:
A = P + P r t, where
- A represents the value of the investment
- P represents the original amount
- r represents the rate in decimal
- t represents the time in years
∵ George deposits $10,000
∴ P = 10,000
∵ First option offers 7.4% per year simple interest
∴ r = 7.4% = 7.4 ÷ 100 = 0.074
∵ He may not withdraw any of the money for three years after
the initial deposit
∴ t = 3
- Substitute all of these values in the formula above
∴ A = 10,000 + 10,000(0.074)(3)
∴ A = 10,000 + 2,220
∴ A = 12,220
The value of the simple interest investment at the end of three years is $12,220
Part B:
, where
- A represents the value of the investment
- P represents the original amount
- r represents the rate in decimal
- n is a number of periods of a year
- t represents the time in years
∵ George deposits $10,000
∴ P = 10,000
∵ The second option offers a 6.5% interest rate compounded quarterly
∴ r = 6.5% = 6.5 ÷ 100 = 0.065
∴ n = 4 ⇒ quarterly
∵ He may not withdraw any of the money for three years after
the initial deposit
∴ t = 3
- Substitute all of these values in the formula above
∴
∴
∴ A = 12,134.08
The value of the compounded quarterly interest investment at the end of three years is $12,134.08
Part C:
∵ 12,220 > 12,134.08
∴ The simplest interest investment is better than the compounded
interest investment at the end of three years
The simple interest investment is better over the first three years
Part D:
I advise George to invest his money in the compounded interest investment if he will keep the money for a long time
Look to the attached graph below
- The red line represents the simple interest investment
- The blue curve represents the compounded interest investment
- (Each 1 unit in the vertical axis represents $1000)
- After 0 years and before 4.179 years the red line is over the blue curve, that means the simple interest is better because it gives more money than the compounded interest
- After that the blue curve is over the red line that means the compounded quarterly is better because it gives more money than the simple interest
Vertex form is
where (h,k) is the vertex.
We can see that the vertex of the graph is at (2,0), and that the graph opens downwards, but does not look stretched at all.
Therefore,
a = -1
h = 2
k = 0
and our vertex form equation is
which is answer A
where (h,k) is the vertex.
We can see that the vertex of the graph is at (2,0), and that the graph opens downwards, but does not look stretched at all.
Therefore,
a = -1
h = 2
k = 0
and our vertex form equation is
which is answer A