Group 1X
6X- Castro, Romina Unice L. December 8, 2010
12X- Gundayao, Angelli Mae M. Case 1: The Time Value of Money
1. The key variables in retirement planning are the following:
The Jordans’ target retirement is at age 65.
Their desired retirement income is $60,000 per year in today’s dollars.
It is expected that Mary and Jordan could expect live up to age 85.
Expected rate of inflation from 1995 to 1998 is 4% per year and there will be no
more inflation in the succeeding years.
2. Given:
n = 3 years
i = 4%
P0 = $60,000
FV3 = P0 (1 + i)3
= $60,000(1 + 0.04)3
= $60,000(1.04)3
= $60,000(1.12486)
= $67,491.84
$67,491.84 is the annual income the Jordans will require at retirement in
three years.
3.
The income stream is an annuity due since there is a constant amount of that will be
received at the beginning of each year.
4. Given:
If i = 8%
PV = A + A (PVIFA8%,19)
= $67,491.84 +$67,491.84(9.60360)
= $67,491.84 + $648,164.5806
= $715,656.4206
If i=8% from 1999 to 2005 then 6% from 2006 to 2018
PV = A + A(PVIFA8%,6) + [A + A(PVIFA6%,12)](PVIF6%,7)
= $67491.84 + $67491.84(4.62288) + [$67491.84 +
$67491.84(8.38384)](0.66506)
= $349,498.4946 + $421,202.5463
= $770,702.0409
5. The sources of Jordans’ retirement income are:
Investment account at ABC Securities
John’s 401(k) plan
John’s IRA
Mary’s IRA
John’s Social Security Retirement Benefits
Mary’s Social Security Retirement Benefits
6.
Annually:
i = 8%
FV3 = P0(FVIF8%,3)
= $160,000 (1 + 0.08)3
= $160,000 (1.08)3
= $160,000 (1.25971)
= $201,553.92
Semiannually:
i = 4%
FV6 = P0(FVIF4%,6)
= $160,000(1 + 0.04)6
= $160,000(1.04)6
= $160,000(1.26532)
= $202,451.0429
7.
John’s IRA
i = 8% annually
FV3 = P0(FVIF8%,3)
= $22,300(1 + 0.08)3
= $22,300(1.08)3
= $22,300(1.25971)
= $28,091.57760
i = 4% semiannually
FV6 = P0(FVIF4%,6)
= $22,300(1 + 0.04)6
= $22,300(1.04)6
= $22,300(1.26532)
= $28,216.61411
Mary’s IRA
i = 8% annually
FV3 = P0(FVIF8%,3)
= $11,000(1 + 0.08)3
= $11,000(1.08)3
= $11,000(1.25971)
= $13,856.832
i = 4% semiannually
FV3 = P0 (FVIF4%,6)
= $11,000(1 + 0.04)6
= $11,000(1.04)6
= $11,000(1.26532)
= $13,918.50920
Effective Annual Interest Rate
= [1 + (i/m)]m – 1
= [1 + (8%/2)]2 – 1
= (1.04)2 – 1
= 1.08160 – 1
= 0.08160
8.
i = 8% expected return, percentage of employer match contribution = 3%, employer
matching contribution = $270, Current 401(k) balance = $86,000, expected annual
addition = $9,000 or 10% of John’s annual salary ($90,000)
Year Beginning John’s Employer FVIF Value on End of
Balance Contribution Matching Year 1998
Contribution
1995 $86000 $9000 $270 1.25971 $120,012.7622
1996 $9000 $270 1.16640 $10,812.528
1997 $9000 $270 1.08 $10,011.60
1998 - - -
Total $140,836.8902
9.
Lump-sum equivalent
John’s: $22,000
Mary’s: $12,000
$34,000/yr
n =20yrs
PV in 1998= ($34,000) (20) (PVIF 8%, 20)
= $680,000(1+0.08)20
= $145,892.7810
Annual payments
First payment given on August 1, 1998, n = 20 periods
Income stream is annuity due.
PV = A + A(PVIFA8%,19)
= $34,000 + $34,000(9.60360)
= $34,000 + $326,522.3728
= $360,522.3728
10.
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