Suppose carla has $12,000 to invest. which investment yields the greater return over 2 years: 9% compounded quarterly or 8.85% compounded monthly? a) the rate of 8.85% compounded monthly is better. b) the rate of 9% compounded quarterly is better. c) they are the same.

B) The rate of 9% compounded quarterly is better

Explanation:

The effective annual rate at 8.85% compounded monthly is ...

... (1 +0.0885/12)^12 -1 ≈ 9.218%

The effective annual rate at 9% compounded quarterly is ...

... (1 +0.09/4)^4 -1 ≈ 9.308% . . . . . . larger than 9.218%

The higher rate compounded less often is better.

The rates would be nearly equivalent (within $1 over 2 years) if the rate compounded monthly were about 8.93% instead of 8.85%

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12