.75 because .75 is .25 from 1.0 and .25 from .5
The interest rate is 6.992%, if a bank advertises that it compounds money quarterly and that it will take Double your money in 10 years.
Step-by-step explanation:
The given is,
Compounds money quarterly
Double your money in 10 years
Step:1
Formula to calculate future investment with compounded quarterly,
...............................(1)
Where, A - Future amount
P - Initial investment\
r - Rate of interest
n - No. of compounding in a year
t - No. of years
Step:2
Let, P = X
A = 2X ( Double your money )
From given, n - 4 ( for compounding quarterly )
t - 10 years
From equation (1)
![2X =X(1+\frac{r}{4} )^{(4)(10)}](https://tex.z-dn.net/?f=2X%20%3DX%281%2B%5Cfrac%7Br%7D%7B4%7D%20%29%5E%7B%284%29%2810%29%7D)
![\frac{2X}{X} =(1+\frac{r}{4} )^{(4)(10)}](https://tex.z-dn.net/?f=%5Cfrac%7B2X%7D%7BX%7D%20%20%3D%281%2B%5Cfrac%7Br%7D%7B4%7D%20%29%5E%7B%284%29%2810%29%7D)
![2 =(1+\frac{r}{4} )^{40}](https://tex.z-dn.net/?f=2%20%20%3D%281%2B%5Cfrac%7Br%7D%7B4%7D%20%29%5E%7B40%7D)
Take root
root on both side,
![\sqrt[40]{2} = (1+\frac{r}{4} )](https://tex.z-dn.net/?f=%5Csqrt%5B40%5D%7B2%7D%20%3D%20%281%2B%5Cfrac%7Br%7D%7B4%7D%20%29)
![1.017479692 = (\frac{4+r}{4} )](https://tex.z-dn.net/?f=1.017479692%20%3D%20%28%5Cfrac%7B4%2Br%7D%7B4%7D%20%29)
![(1.017479692)(4) = (r+4)](https://tex.z-dn.net/?f=%281.017479692%29%284%29%20%3D%20%28r%2B4%29)
![4.06992=(r+4)](https://tex.z-dn.net/?f=4.06992%3D%28r%2B4%29)
![r = 4.06992 -4](https://tex.z-dn.net/?f=r%20%3D%204.06992%20-4)
![r =( 0.06992)(100)](https://tex.z-dn.net/?f=r%20%3D%28%200.06992%29%28100%29)
r = 6.992 %
Result:
The interest rate is 6.992%, if a bank advertises that it compounds money quarterly and that it will take Double your money in 10 years.
Answer: B and E are irrational numbers
Answer:
I don't really know but one triangle is 180 degrees so two added together is 360 degrees...
but ohh I remembered
a=c+d (since a+b=180 and c+d+b=180)
e=g+h (since e+f=180 and g+h+f= 180)
and the fact is that c+d+g+h+b+f=the angle sum of quadrilateral PQRS
a+e+b+f= the angle sum of quadrilateral PQRS (by substitutions)
a+e+b+f=360 (four angles are from one origin so it's 360 degrees )
Y=4x+4
I think this is it u just have to simplify to get it to y=mx+b