Answer:
C) $10,000 invested at 6.7% compounded quarterly over 7 years yields the greater return.
Step-by-step explanation:
-We determine the effective interest rate in both scenarios and use it to calculate the investment's value after 7 years.
#Given n=7yrs, P=$10,000 and i=6.6% compounded monthly:
![i_m=(1+i/m)^m-1\\\\=(1+0.066/12)^{12}-1=0.06803\\\\\therefore A=P(1+i_m)^n\\\\=10000(1.06803)^7\\\\\approx \$15,852.00](https://tex.z-dn.net/?f=i_m%3D%281%2Bi%2Fm%29%5Em-1%5C%5C%5C%5C%3D%281%2B0.066%2F12%29%5E%7B12%7D-1%3D0.06803%5C%5C%5C%5C%5Ctherefore%20A%3DP%281%2Bi_m%29%5En%5C%5C%5C%5C%3D10000%281.06803%29%5E7%5C%5C%5C%5C%5Capprox%20%5C%2415%2C852.00)
#Given n=7rs, P=10000, i=6.7%
![i_m=(1+i/m)^m-1\\\\=(1+0.067/4)^{4}-1=0.06870\\\\\therefore A=P(1+i_m)^n\\\\=10000(1.06870)^7\\\\\approx \$15,921.75](https://tex.z-dn.net/?f=i_m%3D%281%2Bi%2Fm%29%5Em-1%5C%5C%5C%5C%3D%281%2B0.067%2F4%29%5E%7B4%7D-1%3D0.06870%5C%5C%5C%5C%5Ctherefore%20A%3DP%281%2Bi_m%29%5En%5C%5C%5C%5C%3D10000%281.06870%29%5E7%5C%5C%5C%5C%5Capprox%20%5C%2415%2C921.75)
Hence, the investment has the largest value($15,921.75) when the interest rate is compounded quarterly.
Twelve, two hundred and fourty five
Answer:
See the proof below
Step-by-step explanation:
Let the line AB be a straight line on the parallelogram.
A dissection of the line (using the perpendicular line X) gives:
AY ≅ BX
Another way will be using the angles.
The angles are equal - vertically opposite angles
Hence the line AY ≅ BX (Proved)
Answer:
mx -y = 4m -7
Step-by-step explanation:
Standard form is ...
ax +by = c
where a, b, c are mutually prime integers and a > 0.
If we assume m > 0, then we need to collect the variable terms on the right side of the equation, so the coefficient of x will be positive.
y -7 = mx -4m . . . . eliminate parentheses
-7 = mx -y -4m . . . . subtract y
4m -7 = mx -y . . . . . add 4m
mx -y = 4m -7 . . . . . . standard form