1)

Option (d) is correct

Here, the withdrawals will be same every month, so it is an annuity. We need to calculate the present value of annuity by the following formula:

PVA = P * (1 - (1 + r)^-n / r)

where, PVA = Present value of annuity, P is the periodical amount = $1000, r is the rate of interest = 7%, so monthly rate = 7% / 12 = 0.58333% and n is the time period = 20 * 12 = 240 months

Now, putting these values in the above formula, we get,

PVA = $1000 * (1 - (1 + 0.58333%)^-240 / 0.58333%)

PVA = $1000 * (1 - ( 1+ 0.0058333)^-240 / 0.0058333)

PVA = $1000 * (1 - ( 1.00583333)^-240 / 0.0058333)

PVA = $1000 * (1 - 0.24760204543) / 0.0058333)

PVA = $1000 * (0.75239795456 / 0.0058333)

PVA = $1000 * 128.982580

PVA = $128983

So, she need to have $128983 in her retirement account.

2)

money in her retirement account today

=1000*((1-(1+(7%/12))^(-20*12))/(7%/12))=128983

the above will be answer

3)

she wants to withdraw per month 1000 then for 20 years 240000/-

She is expecting 7% average rate of return

answer is option e i.e 1,78,451.

So she need to maintain 1,78,451/- today in her retirement savings account to withdraw 1000 per month for 20 years.

4)

We can calculate the desired result as follows:

Semi Annnual Payments (pmt) = $ 6,200

Period = 4 years

Semi Annual Period (nper) = 8

Annual interest rate = 7.20%

Semi Annual interest rate = 7.20% / 2

Semi Annual interest rate (rate) = 3.60%

First we will calculate the Present value of ordinary annuity which is the value at 7 years from now that is amount :

= PV(rate, nper, -pmt)

= PV(3.6%, 8, -6200)

= $ 42,441.21

Value of Annuity ( 7 - 3 ) 4 years from now is the ordinary annuity discounted back by 3 years which is calculated as follows:

Future Value (fv) = $ 42,441.21

Semi Annual Period (nper) = 3 * 2 = 6

Semi Annual interest rate (rate) = 3.60%

= PV(rate, nper, -pmt, -fv)

= PV(3.6%, 8, 0, -42441.21)

= $ 34,326.48

So, the value of annuity 4 years from now is $ 34,326 and the correct answer is option (a)