Sum of $1000 was invested for 4 years, and the interest was compounded semiannually. If this sum amounted to $1389.08 in the giv
1 answer:
The answer is 8%
Compound interest formula is:
A = P(1 + r/n)ⁿˣ
A - the final amount
P - the initial amount
r - interest rate
n - number of compoundings per year
x - time period
We have:
A = <span>$1389.08
P = </span><span>$1000
r = ?
n = 2 (it is semiannual)
x = 4
</span>A = P(1 + r/n)ⁿˣ
1389.08 = 1000(1 + r/2)²*⁴
1389.08 = 1000(1 + r/2)⁸
(1 + r/2)⁸ = 1389.08/1000
(1 + r/2)⁸ = 1.389
![\sqrt[8]{(1 + \frac{r}{2} ) ^{8}} = \sqrt[8]{1.389} \\ 1 + \frac{r}{2} =1.04 \\ \frac{r}{2} = 1.04-1 \\ \frac{r}{2} = 0.04 \\ r = 2*0.04 =0.08](https://tex.z-dn.net/?f=%20%5Csqrt%5B8%5D%7B%281%20%2B%20%20%5Cfrac%7Br%7D%7B2%7D%20%29%20%5E%7B8%7D%7D%20%20%20%3D%20%20%5Csqrt%5B8%5D%7B1.389%7D%20%20%5C%5C%20%0A1%20%2B%20%20%5Cfrac%7Br%7D%7B2%7D%20%3D1.04%20%5C%5C%20%0A%20%5Cfrac%7Br%7D%7B2%7D%20%3D%201.04-1%20%5C%5C%20%0A%20%5Cfrac%7Br%7D%7B2%7D%20%3D%200.04%20%5C%5C%20%0Ar%20%3D%202%2A0.04%20%3D0.08)
r = 0.08 = 8/100 = 8%
Compound interest formula is:
A = P(1 + r/n)ⁿˣ
A - the final amount
P - the initial amount
r - interest rate
n - number of compoundings per year
x - time period
We have:
A = <span>$1389.08
P = </span><span>$1000
r = ?
n = 2 (it is semiannual)
x = 4
</span>A = P(1 + r/n)ⁿˣ
1389.08 = 1000(1 + r/2)²*⁴
1389.08 = 1000(1 + r/2)⁸
(1 + r/2)⁸ = 1389.08/1000
(1 + r/2)⁸ = 1.389
r = 0.08 = 8/100 = 8%
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The estimated standard deviation from the range rule is 145.5 cm3.As it is 29.8 cm3 smaller than the exact standard deviation, we consider that the estimation is not accurate enough.
Generally, brain volumes which are smaller than 921.1 cm3 can be considered significantly low and bigger than 1417.5 cm3 can be considered significantly high. Hence, brain volume of 1457.5 cm3 is bigger than the expected maximum, so it can be considered significantly high.
The calculation goes like this,
According to the range rule, the standard deviation and range, or the distance between the maximum and smallest value, are roughly inversely proportional:
If we have a sample of 50 brains volumes, and they range from 910 cm3 to 1492 cm3, we can estimate the standard deviation as:
s=1492-910/4=582/4=145.5
The exact standard deviation is 175.3 cm3.The difference is 175.3-145.5=29.8 cm3, so the estimation is not accurate enough.
The range rule of thumb states that we should anticipate a maximum value that is approximately two standard deviations above the mean and a lowest value that is approximately two standard deviations below the mean. The expected ranges are as follows given our mean volume of 1169.3 cm3 and standard deviation of 124.1 cm3:
Min= M-2s=1169.3-2*124.1=921.1
Max=M+2s=1169.3+2*124.1=1417.5
The brain capacity of 1457.5 cm3 can be regarded as significantly high because it is higher than the predicted maximum.
To know about standard deviation click here :
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