1)How much money does Marta need to have in her retirement savings account today if she wishes to withdraw $1,000 a month for 20 years? She expects to earn an average rate of return of 7 percent

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)