A 15-year annuity pays $1,475 per month, and payments are made at the end of each month. If the interest rate is 9 percent compounded monthly for the first seven years, and 6 percent compounded monthly thereafter, what is the present value of the annuity? (Do not round intermediate calculations and round your answer to 2 decimal places, e. g., 32.16.)

Explanation:

First of all we shall calculate the present value of an annuity( at the end of 7 years )  of 1475

at interest rate of 6/12 = .5 % for total instalment of 12 x 8 = 96 ( 6% compounded monthly )

rate of intt .5% , no of instalment 96

PV of annuity of 1475

= 112252.66

This amount has to be discounted at 9 % to present value for 7 years

or calculated at 9/12 = .75% for 84 instalment

PV of 112252.66

= 59925.55

Now , we shall calculate PV of annuity of 1475 for 7 years compounted monthly ( rate of intt .75 % , no of instalment 84)

PV of annuity of 1475

= 91671.84

Total value

= 59925.55 + 91671.84

= 151597.39

answer; encouraging the development of innovations by firms attempting to break a monopoly; (creative destruction)

start by isolating the variable on one side by adding 43w^2 to both sides.   the equation will read:

25w^2+5=0

*subtract 5 from both sides*

25w^2=-5

*divide both sides by 25*

w^2=-1/5

*take the square root of both sides*

w=√(-1/5)

the square root of -1 is i.   the square root of 5 remains √5

the answer is i/√5.

hope this