A=P (1+r/n)^nt
A= Total amount invested, P=principal amount, r=Interest rate, n=number of time in a year when the interest is earned (for annual, n=1; for semi-annual, n=2, ...), t = time in years
In the current scenario, case 1, n=2; case 2, n=1 and A1=A2, t1=t2
Therefore,
800(1+0.0698/2)^2t = 1000(1+0.0543/1)t
Dividing by 800 on both sides;
(1+0.0349)^2t = 1.25(1+0.02715)^t
(1.0349)^2t = 1.25(1.02715)^t
Taking ln on both sides of the above equation;
2t*ln (1.0349)= ln 1.25 + t*ln (1.02715)
2t*0.0343 = 0.2231+ t*0.0268
0.0686 t = 0.2231+0.0268 t
(0.0686-0.0268)t = 0.2231
0.0418t=0.2231
t=5.337 years
Therefore, after 5.337 years or 5 years and approximately 4 months, their value of investments will be equal.
This value will be,
A=800(1+0.0698/2)^2*5.337 = $1,153.76
Answer:
42
Step-by-step explanation:
One angle of a regular pentagon = 108°
One angle of a regular hexagon = 120°.
One angle of a square = 90°
∴ ∠BAC = 360 – (108 + 20 + 90) 360 – 318 = 42°
Answer:8
Step-by-step explanation:
Answer:
x = 170 deg
Step-by-step explanation:
A tangent to a circle is perpendicular to the radius of the circle at the point of tangency. That means that in quadrilateral AOBC, angles A and B are right angles and measure 90 deg.
The sum of the measures of the angles of an n-sided polygon is
(n - 2)180 deg
In this case, n = 4, so
(4 - 2)180 deg = 360 deg
m<A + m<O + m<B + m<C = 360
90 + x + 90 + 10 = 360
x + 190 = 360
x = 170
Answer: 170 deg
