Age:21 Year Until retirement: 42 Years in retirement: 28 inflation assumption: 3
ID: 2775177 • Letter: A
Question
Age:21
Year Until retirement: 42
Years in retirement: 28
inflation assumption: 3.6%
Return during savings:12.0%
Return during retirement: 5.0%
annual raises:3.5%
current income: 63,000
income in 22 years: ____ assuming 3.5% raises year over year
current retirement savings: 0
annual contribution to retirement: 6300
first half of years to retirement: 6000
second half of years to retirement: 0
1. How much will the client be able to withdraw each year of retirement, if the client wants to leave an amount equal to 20% of the starting amount of the retirement account on day retires (so 20% of $6,075,465), to hiers upon his death which he assumes will be the last day of his projected retirement (so this will be a lump sum at the end)? (please show the financial calculator inputs)
2. Now create a worst case scenerio for your client. You are now half way to retirement:
A.) Assume the returns for the first half of the savings period are 2% less than assumed above, and the client only put away half of what was assumed. (please show the financial calculator inputs)
B.) How much will the client have to now save per year to save to the orginal amount found in part a, assuming the rate goes back to the assumed return during savings period? (please show the financial calculator inputs)
Explanation / Answer
Current Age – 21
Years until retirement – 42
Years in retirement - 28
Inflation rate = 3.6%
Return during savings = 12%
Return during retirement = 5%
Annual rises = 3.5%
Current Income = 63000
Income in 22 years assuming 3.5% rise year over year = 63000 * 1.035^22 = 63000 * 2.1315116
= 134,285.23
Current retirement savings = 0
Annual Contribution to retirement = 6300
Total Retirement savings at the time of retirement = 6300 * [(1+0.12)^42 -1]/0.12
= 6300 *[116.7231 – 1] / 0.12
= 6300 * (115.7231/0.12)
= 6300 * 964.3595
= 6,075,464.85 or 6,075,465 (rounded off)
If the contribution during the first half of years to retirement (42/2) 21 years is 6000, then the Future value of contribution at the end of the 21 years
FV = 6000 * [(1.12^21 -1]/0.12 = 6000 * [10.80385 – 1]/0.12 = 6000 * (9.80385/0.12)
= 6000 * 81.6987 = 490,192.20 or 490,192 (rounded off)
Annual contribution (A) to be made during the second half of time to retirement which is 21 years to have a final value of 6,075,465 can be calculated as follows
6,075,465 = A * [(1+0.12)^21 -1]/0.12 + 490,192 * 1.12^21
6,075,465 = A * 81.6987 + 490192 * 10.80385
6,075,465 = A * 81.6987 + 5,295,960 (Actual value 5,295,959.988)
81.6987 * A = 6,075,465 – 5,295,960 = 779,505
A = 779,505/81.6987 = 9,541.21 or 9,541
The amount to be contributed during the second half of period to retirement is 9,541
Answer (1)
Amount left to heirs = 20% of the starting retirement amount = 6,075,465 * 0.20
= 1,215,093
Balance amount available = 6,075,465 – 1,215,093 = 4,860,372
Return during retirement = 5% or 0.05
Let P be the annual withdrawal during the post retirement period of 28 years. P can be calculated as follows
4,860,372 = P * [1-(1/(1+0.05)^28]/0.05
4,860,372 = P * [1-1/3.920129]/0.05
4,860,372 = P * [1-0.255094]/0.05
4,860,372 = P * (0.74491/0.05)
4,860,372 = P * 14.898127
P = 4860372/14.898127 = 326,240.47 or 326,240 (rounded off)
The annul amount which can be withdrawn after leaving 20% of initial retirement savings to heirs is 326,240
Answer (2) (a)
Returns for the first half of retirement period = 12 – 2 = 10% or 0.10
Annual contribution to retirement savings during first half of years to retirement = 3000
FV = 3000 * [(1.10^21 -1]/0.10 = 3000 * [7.4003 – 1]/0.10 = 3000 * (6.4003/0.10)
= 3000 * 64.003 = 192,009
The savings during the first half of period to retirement would be 192,009
Answer (2)(b)
Returns on savings = 12%
Remaining period to retirement = 21 years
Target savings amount = 6,075,465
Current savings amount = 192,009
Let A be the amount to be saved per annum to reach the target savings amount
6,075,465 = A * [(1+0.12)^21 -1]/0.12 + 192,009 * 1.12^21
6,075,465 = A * 81.6987 + 192,009 * 10.80385
6,075,465 = A * 81.6987 + 2,074,436
A = (6,075,465 – 2,074,436)/81.6987 = 4,,001,029 /81.6987 = 48,972.98 or 48,973 (rounded off)
Amount to be saved annually during the second half of time to retirement to reach targeted retirement savings is 48,973
Inputs for Financial Calculator as required
Income in 22 years assuming 3.5% rise year over year = 63000 * 1.035^22 = 134,285.23
In Finance Calculator
N (# of Periods) = 42
Start Principal = 0
I/Y (interest) = 12%
PMT = 6300
PMT mode ending
Calculate will give answer FV 6,075,464.71
Total Retirement savings at the time of retirement
In Finance Calculator
N (# of Periods) = 42
Start Principal = 0
I/Y (interest) = 12%
PMT = 6300
PMT mode ending
Calculate will give answer FV 6,075,464.71
If the contribution during the first half of years to retirement (42/2) 21 years is 6000, then the Future value of contribution at the end of the 21 years
In Finance Calculator
N (# of Periods) = 21
Start Principal = 0
I/Y (interest) = 12%
PMT = 6000
PMT mode ending
Calculate will give answer FV 490,192.41
Annual contribution (A) to be made during the second half of time to retirement which is 21 years to have a final value of 6,075,465 can be calculated as follows
In Finance Calculator (PMT function)
FV = 6075465
N (# of Periods) = 21
Start Principal = 490192
I/Y (interest) = 12%
PMT mode ending
Calculate will give answer PMT 9,541.22
The annul amount which can be withdrawn after leaving 20% of initial retirement savings to heirs (annuity pay out calculator). Input in Finance Calculator
Starting Principle = 4860372
Interest Rate = 5%
Inflation Rate = 0
Years to Payout = 28
Payout Frequency = Yearly
Calculate will give you 326,240.47
In case you include inflation rate as 3.6% then the answer will be still same
Answer (2)
The savings during the first half of period to retirement would be
In Finance Calculator
N (# of Periods) = 21
Start Principal = 0
I/Y (interest) = 10%
PMT = 3000
PMT mode ending
Calculate will give answer FV 192,007.50
Amount to be saved annually during the second half of time to retirement to reach targeted retirement savings is 48,973
In Finance Calculator (PMT function)
FV = 6075465
N (# of Periods) = 21
Start Principal = 192008
I/Y (interest) = 12%
PMT mode ending
Calculate will give answer PMT 48973.09