the present value of a series of payments of 2000 at the end of every four quarter, forever, is equal to 5000. calculate the effective rate of interest per quarter

The effective rate of interest per quarter is 40%.

Step-by-step explanation:

This can be calculated using the formula for calculating the Present Value of a Perpetuity as follows:

PV = A / r (1)

Where;

PV = Present value of the series of payments = $5,000

A = Quarterly payment = $2,000

r = Quarterly effective rate of interest = ?

Substituting the values into equation (1) and solve for r, we have:

5,000 = 2000 / r

5,000 * r = 2,000

r = 2,000 / 5,000

r = 0.40, or 40%

Therefore, the effective rate of interest per quarter is 40%.

irst, find the z score of a score of 80. this is given by the formula z = (x-u)/o, where x is the score, u is the mean, and o is the standard deviation. this gives

z = (80-78)/12 = 1/6 = .1667

now, find what percentile a z score of 1/6 correlates to in the normal distribution.

a z score of 1/6 = .1667 is equivalent to the 56.36th percentile of the distribution. so the probability a score is over this is 1-.5636 = .4364

the mean of a sample mean is equal to the original mean. however, the standard deviation of a sample mean is equal to the original standard deviation divided by the square root of n (sample size). so the new standard deviation is 12/sqrt(16) = 3.

the new z score is 80-78/3 = 2/3 = .667. this is equivalent to the 74.86th percentile. so the probability that the mean will be greater than this score is 1-.7486 = .2514.

4n=2m

ratio of m to n: 2/4 = 1/2

answer

a. 1/2