The compound amount and the interest earned are $13,222.17 and $2,222.17 respectively.
<h3>What is compound interest?</h3>
It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.
We can calculate the compound interest using the below formula:
![\rm A = P(1+\dfrac{r}{n})^{nt}](https://tex.z-dn.net/?f=%5Crm%20A%20%3D%20P%281%2B%5Cdfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D)
Where A = Final amount
P = Principal amount
r = annual rate of interest
n = how many times interest is compounded per year
t = How long the money is deposited or borrowed (in years)
We know the formula for continuous compounding:
![\rm A = P(e)^{rt}](https://tex.z-dn.net/?f=%5Crm%20A%20%3D%20P%28e%29%5E%7Brt%7D)
![\rm A = 11000(e)^{0.023\times8}](https://tex.z-dn.net/?f=%5Crm%20A%20%3D%2011000%28e%29%5E%7B0.023%5Ctimes8%7D)
A = $13,222.17
I = A - P = 13,222.17 - 11000
I = $2,222.17
Thus, the compound amount and the interest earned are $13,222.17 and $2,222.17 respectively.
Learn more about the compound interest here:
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Answer:
JKM is 123 degrees and the measure of arc KL is 56
Alright, I'm pretty sure I can help.
Let's look at the first answer choice.
7 - 2 (m + 1)
Distribute -2 and add the remaining numbers to get the total for that answer choice.
7 - 2m - 2
Simplify. You get 5 - 2m.
Looks like we found the answer on the first choice!
The Final Answer is 7 - 2 (m + 1)
Answer:
45.2
Step-by-step explanation:
Explanation:
The idea here is that you need to use the mass of water, the heat added to the sample, and the specific heat of water to find the resulting change in temperature.
The equation that establishes a relationship between heat absorbed and change in temperature looks like this
q
=
m
⋅
c
⋅
Δ
T
, where
q
- heat absorbed
m
- the mass of the sample
c
- the specific heat of water, equal to
4.18
J
g
∘
C
Δ
T
- the change in temperature, defined as final temperature minus initial temperature
Plug in your values and solve for
Δ
T
- do not forget to convert the added heat from kilojoules to Joules
q
=
m
⋅
c
⋅
Δ
T
⇒
Δ
T
=
q
m
⋅
c
Δ
T
=
1.0
⋅
10
3
J
50.0
g
⋅
4.18
J
g
∘
C
=
4.785
∘
C
So, if the temperature of the water changed by
4.785
∘
C
, and its final temperature is now
50.0
∘
C
, it follows that its initial temperature was
Δ
T
=
T
f
−
T
i
⇒
T
i
=
T
f
−
Δ
T
T
i
=
50.0
∘
C
−
4.785
∘
C
=
45.2
∘
C