Question

Ann E. Belle is age 45 and plans to retire in 20 years (at age 65). She has retirement savings in a mutual fund account, which has a current balance of $150,000 (Ann does not plan to add any additional money to this account). Also, Ann opened a 401K retirement account with her new employer and will contribute $15,000 per year into her 401K until retirement.

solve question algebraically and show work.

1.)If Ann’s 401K account grows at an annual rate of 8.0% per year, how much money will Ann have in her 401K account at age 65?

2.) at retirement, Ann plans take the investment balance from her mutual fund account and the balance from her 401K account and combine them into an IRA account. To minimize risk, her IRA account will invest in more conservative securities. As a result, Ann anticipates her annual IRA returns to be about 5.0% during retirement.   While in retirement, Susan plans to withdraw $100,000 per year from her IRA account over the next 25 years. Is this possible? Explain why or why not?

Answer 1

PV of annuity for making pthly payment
P = PMT x (((1-(1 + r) ^- n)) / r)
Where:
P = the present value of an annuity stream	A
PMT = the dollar amount of each annuity payment	$         100,000
r = the effective interest rate (also known as the discount rate)	5%
n = the number of periods in which payments will be made	25
PV of retirement corpus needed=	PMT x (((1-(1 + r) ^- n)) / r)
PV of retirement corpus needed=	100000* (((1-(1 + 5%) ^-25)) / 5%)
PV of retirement corpus needed=	$ 1,409,394.46
So the retirement corpus required is $ 1,409,394.46.
Funding source	Mutual Fund
Current balance	$         150,000
Interest	8%
Time	20
Amount at the time of retirement	150000*(1+8%)^20
Amount at the time of retirement	$    699,143.57
Remaining corpus required=	1409394.46-699143.57
Remaining corpus required=	$    710,250.89
Funding source	401(K) Fund
FV of annuity
P = PMT x ((((1 + r) ^ n) - 1) / r)
Where:
P = the future value of an annuity stream	A
PMT = the dollar amount of each annuity payment	$           15,000
r = the effective interest rate (also known as the discount rate)	8%
n = the number of periods in which payments will be made	20
FV of annuity=	PMT x ((((1 + r) ^ n) - 1) / r)
FV of annuity=	15000* ((((1 + 8%) ^20) - 1) / 8%)
FV of annuity=	$    686,429.46
As we can see that the FV of annuity does not provide the requisite FV, it is not possible to set up this arrangement.