1. K. Herrmann has decided to set up a scholarship fund for students. She is wil
ID: 2502517 • Letter: 1
Question
1. K. Herrmann has decided to set up a scholarship fund for students. She is willing to deposit $5,000 in a trust fund at the end of each year for 10 years. She wants the trust fund to then pay annual scholarships at the end of each year for 30 years.
2. Charles Jordy is planning to save for his retirement. He has decided that he can save $3,000 at the end of each year for the next 10 years, $5,000 at the end of each year for Years 11 through 20, and $10,000 at the end of each year for Years 21 through 30.
3. Patricia Karpas has $200,000 in savings on the day she retires. She intends to spend $2,000 per month traveling around the world for the next 2 years, during which time her savings will earn 18%, compounded monthly. For the next 5 years, she intends to spend $6,000 every 6 months, during which time her savings will earn 12%, compounded semiannually. For the rest of her life expectancy of 15 years, she wants an annuity to cover her living costs. During this period, her savings will earn 10% compounded annually. Assume that all payments occur at the end of each period.
Required:
1. In Situation 1, how much will the annual scholarships be if the fund can earn 6%? How much at 10%?
2. In Situation 2,
(a) How much will Charles have at the end of 30 years if his savings can earn 10%? How much at 6%?
(b) If Charles expects to live for 20 years in retirement, how much can he withdraw from his savings at the end of each year if his savings earn 10%? How much at 6%?
(c) How much would Charles need to invest today to have the same amount available at the time he retires as calculated in Situation 2(a) at 10%? How much at 6%?
3. In Situation 3, how much will Patricias annuity be?
Explanation / Answer
N is number of periods
r= rate of interest
PMT=payment
FV=future value
PV=present value.
1) r=6%
for first 10 years
r=6% N =10 PMT=5000 PV=
SO FV=65904
For next 30 years
N=30 I =6% PV=65904 FV=0
So PMT 4788
so scholarship will be $4788/year
##############
if r=10%
for first 10 years
r=10% N =10 PMT=5000 PV=
SO FV=$79687
For next 30 years
N=30 I =6% PV=$79687 FV=0
So PMT 8453
so scholarship will be $8453/year
2)a) for 10 years= saving $3000/year
for next 10 year $5,000
for next 10 year $10,000
taking r=10%
for first 10 year
N=10 r=10 PMT=3000 PV=0
so FV=47812
FOr next 10 year
N=10 r=10 PMT=5000 PV=47812
so FV=203700
for next 10 year
N=10 r=10 PMT=10000 PV=203700
so FV=$687720 at the end of 30 years
##############
taking r=6%
for first 10 year
N=10 r=6 PMT=3000 PV=0
so FV=39542
FOr next 10 year
N=10 r=6 PMT=5000 PV=39542
so FV=136717
for next 10 year
N=10 r=6 PMT=10000 PV=136717
so FV=$376647 at the end of 30 years
....................
b)for 20 years on retirement
if r=10%
N=20 r=10 PV=687720 FV=0
so PMT=$80780/year
#############
if r=6%
N=20 r=6 PV=376647 FV=0
so PMT=$32837/year
..............
c)
for =10%
N=30 r=10 FV=687720 PMT=0
so PV=$394122 to be deposted at today
#########
for r=6%
N=30 r=6% FV=$376647 PMT=0
so PV=$65578 to be deposted at today
3)for next two year
PV=$200,000
spending= $2,000 per month
and r=18% compunded monthly
so N=2*12
r=18/12 % monthly
so N=24 r=1.5 PMT= -2000 PV=20000
so FV=$228633.5
for next 5 years
spend $6,000 every 6 months, r= 12% componded semi-semiannually.
so N=2*5 r=12/2 % and PMT=- $ 6000
PV=$228633.5 so
FV=$330362
for next 15 years
N=10 r=10% PV=$330362 FV=0
so PMT=$53765
so annuity be $$53765 per year
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