Question

Please Answer ALL PARTS To The Question!!!

3. yn hawe just gradvated from college and started yaw new job. To ensure you have the finds you need for retirement you have decided to invest 11,500 in a brokerage aciant each year towards yar Nehrenent Yuw first payment will be made at the end of this year. Assume you work for to years. If yw can invest at 12 percent nominal interest rate, how much will you have in your account when you retine in to years? Once retired, you more you retirement savings to a less sky portfolio that pays only 6 percent. Il yw withdraw 184,00 per year from your retirement acant, how many years will yar retrennt funds last?

Answer 1

Compute the PVIFA at 12% and 40 years, using the equation as shown below:

PVIFA = {1 – (1 + Rate)^{-Number of periods}}/ Rate

                   = {1 – (1 + 0.12)^-40}/ 12%

            = 8.243776682

Hence, the PVIFA at 12% and 40 years is 8.243776682.

Compute the PVIF at 12% and 40 years, using the equation as shown below:

PVIF = 1/ (1 + Rate)^{Number of periods}

              = 1/ (1 + 0.12)⁴⁰

         = 0.01074679818

Hence, the PVIF at 12% and 40 years is 0.01074679818.

Compute the amount in retirement account at the time of retirement, using the equation as shown below:

Future value = Annual savings*PVIFA_{12%, 40 years}/ PVIF_{12%, 40 years}

                     = $1,500*8.243776682/ 0.01074679818

                     = $1,150,637.131

Hence, the amount in retirement account at the time of retirement is $115,0637.131.

Compute the PVIFA, using the equation as shown below:

PVIFA = Value of investment at retirement/ Annual withdrawal

             = $1,150,637.131/ $84,000

             = 13.69806108

Hence, the PVIFA is 13.69806108.

Compute the time taken to exhaust the savings, using the equation as shown below:

           PVIFA = {1 – (1 + Rate)^{-Number of periods}}/ Rate

   13.69806108= {1 – (1 + 0.12)^{- Number of periods} }/ 12%

13.69806108 * 12% = {1 – (1.12)^{- Number of periods} }

1.64376733                = {1 – (1.12)^{- Number of periods} }

(1.12)^{- Number of periods}   = 1 – 1.64376733

(1.12)^{- Number of periods}    = 0.64376733

Taking log both sides

- Number of periods * log ( 1.12) = log (0.64376733)

Number of periods                         = - log (0.64376733)/ log ( 1.12)

Number of periods                         = 3.886199737

Hence, the time taken to exhaust the savings is 3.886199737.

Answer 2

Answer
I	Values from Question
	Yearly Investment	$          1,500.00
	No.of Years	40
	Rate of Interest	12%
	Amount in account at the time of retirement. That means future value of annuity at the time of 40 th year
	Future Value of Annuity (FVA) = Annuity * (1+r)^n - 1 / r
	Annuity=	$          1,500.00
	r=	12%
	n=	40
	FVA =	1500 * (1+.12)^40 -1 / .12
		$ 1,150,637.13
	Amount in account at the time of retirement = $1,150,637/-
II	Withdrawal per year = 84,000
	Present Value of Annuity = 1,150637
	Interest rate 6%
	PVA =	A * ( 1 + r )^n - 1 / r*(1+r)^n
	1,150637 = 84000 * (1.06)^n - 1 / .06*(1.06)^n
	13.69 = 1.06^n - 1 / .0636^n
	= 30 Years