Description
P5-36 Changing compounding frequency. Using annual, semiannual, and quarterly compounding periods for each of the following, (1) Calculate the future value if $5000 is depositing initially and (2) determine the effective annual rate (EAR). a. at 12% annual interest for 5 years. b. at 16% annual interest for 6 years. c. at 20% annual interest for 10 years. P5-43 Creating a retirement fund. To Supplement your planned retirement in exactly 42 years, you estimate that you need to accumulate $220,000 by the end of 42 years from today. You plan to make equal, annual, end of the year deposits into an account paying 8% annual interest. a. How long must the annual deposits be to create the $220,000 fund by the end of 42 years? b. If you can afford to deposit only $600 per year into the account, how much will you have accumulated by the end of the 42 year? P5-48 Loan amortization schedule. Joan Messineo borrowed $15,000 at 14% annual rate of interest to be repaid over 3 years. The loan amoritized into 3 equal , annual, end of the year payments. a. Calculate the annual, end of the year loan payment. b. Prepare the loan amortization schedule showing interest and principal breakdown of each of the 3 loan payments. c. Explain why the interest portion of each payment declines with the passage of time. Show all work.
Uma Corp.
Present Value of Expected Future Saving
Period: 2016 through 2026
Discount rate for years 2016 – 2021
Discount rate for years 2022 – 2026
Year
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
Period
1
2
3
4
5
6
7
8
9
10
11
Annual
Savings
-2000
120000
130000
150000
160000
150000
90000
90000
90000
90000
90000
=SUM(C10:C20)
PV Lump Sum
=C10/(1+$E$5)^B10
=C11/(1+$E$5)^B11
=C12/(1+$E$5)^B12
=C13/(1+$E$5)^B13
=C14/(1+$E$5)^B14
=C15/(1+$E$5)^B15
Uma Corp.
Present Value of Expected Future Savings
Period: 2016 through 2026
0.07
0.11
PV Annuity
=C16*((1-(1/(1+$E$6)^B14))/$E$6)
PV Lump Sum
=E16/(1+$E$5)^B15
Present
Value
=D10
=D11
=D12
=D13
=D14
=D15
=F16
=SUM(G10:G20)
P5-3 Future Value
PV
I
FV
###### ######
0.12
0.06
###### ######
N
6.1163 11.896
Time does not double the time but it comes close. The compounding affect on the time value of money i
Final Value = initial value(1+interest rate)time
200=100(1+0.12)n
200=100(1.0.06)n
ut it comes close. The compounding affect on the time value of money is the reason the time was not doubled.
P5-5
FV3= -1500(1.07)3Fv6=-1500(1.07)6 FV9=1500(1.07)9
a.
Future Value of a single ammount (FV)
Present Value (PV)
($1,500)
($1,500)
($1,500)
Annual Rate of Interest ( r )
7.00%
7.00%
7.00%
Number of Periods (n)
3
6
9
Future Value
b.Interest Earned FV-PV
($1,837.56)
($2,251.10)
($2,757.69)
$337.57
$413.53
$506.59
c. It is a longer period of time causing more compounded interest
P5-12
a.
PV=FV/(1+r) n
PV=6000/(1+.12)6
PV=6000/ (1.97382)
#########
They need to invest $3039.79 today to be worth $6000 in six years.
b.
PV=FV/(1+r)n
6000/(1+0.12)6
6000/(1.12)6
6000/(1.97382)
#########
c.
PV=FV/(1+r) n
PV=6000/(1+.12)6
PV=6000/ (1.97382)
#########
Each problem had the same given data, so the answers were all exactly like. The same formula was used with each
mula was used with each problem.
Time Value
P5-13
PV= FVn/(1+r)n
a.
$500/(1+0.07)3
($408.15)
b.The most he can pay is $408.15 for this payment. I would use the same formula from a to find this
c. If he invests less and still gets paid $500 three years from today, it would mean his rate of return
d mean his rate of return is higher on this ivestment.
P5-20
Amount of annuity
A
B
C
D
E
Formulas
Work
Interest rate
$12,000
$55,000
$700
$140,000
$22,500
7.00%
12.00%
20.00%
5.00%
10.00%
Ordinary Annuity Present Value
PVn=(CF/r)x[1-1/(1+r)n
a.
(12000/.07)x[1-1/(1+.07)3]
(171,428.57)x[1-1/1.225043]
171,428.57x[1-.81629]
171,428.57x.18371
$31,491.79
Annuity Due Present Value
3
PVn=(CF/r)x[1-1/(1+r)n]x(1+r) a.(12000/.07)x[1-1/(1+.07) ]x(1+.07)
(171428.57)x[1-.81629]x1.07
171428.57x.1837×1.07
$33,696.00
B Ordinary annuity is less than value of annuity due. This fact makes oridinary annuity better because the payment o
Period (years)
3
15
9
7
5
b.
PV ordinary annuity.
PV annuity due
($31,491.79)
($374,597.55)
($2,821.68)
($810,092.28)
($85,292.70)
c.
15
(55000/.12)x[1-1/(1+.12) ]
d.
9
(700/.20)x[1-1/(1+.20) ]
(458,333.33)x [1-1/(5.47)]
(3500)x[1-1/(5.15)]
458,333.33x [1-.18269]
3500x[1-.19380]
458,333.33x .8173
3500x.8062
$374,597.54
($33,696.22)
($419,549.25)
($3,386.01)
($850,596.89)
($93,821.97)
(140000/.05)x[1-1/(1+.05)7]
(2,800,000)x[1-1/1.407]
2800000x[1-.7106]
2800000x.2893
$2,821.68
$810,092.28
b.(55000/.12)x[1-1/(1+.12)15]x(1+.12)
c.(700/.20)x[1-1/(1+.20)9]x(1+.20)d.(140000/.05)x[1-1/(1+.05)7]x(1+.05)
(458333.33)x[1-.18269]x1.12
(3500)x[1-.19380]x1.2
(2800000)x[1-.71068]x1.05
458333.33x.8173×1.12
3500x.8062×1.2
2800000x.2893×1.05
$419,549.25
$3,386.01
$850,596.89
fact makes oridinary annuity better because the payment of the annuity is made at years end, whereas in annuity due the payment is made a
Difference
($2,204.43)
($44,951.71)
($564.34)
($40,504.61)
($8,529.27)
e.
(22500/.10)x[1-1/(1+.10)5]
(225,000)x[1-1/1.61]
225000x[1-.6209]
225000x.3790
$85,292.70
e.(22500/.10)x[1-1/(1+.10)5]x(1+.10)
(225,000)x[1-.6209]x(1.10)
225000x03790x1.10
$93,821.97
n annuity due the payment is made at the beginning of the year. The amount invested would be for one extra year.
P5-24
Formula PVn=(CF/r)x[1-1/(1+r)n}
a. PV
Intererst rate ( r )
Number of Periods (n)
Annuity Payment (PMT)
Present Value
b.PV
Interest Rate ( r )
Numner of periods (n)
Annunity Payment (PMT)
11% )
30
-20000
a. (-20000/.11)x{1-1/(1+.11)30}
(-181818.19)x(1-.04368)
$173,875.85
9%
30
-20000
b.(-20000/.09)x{1-1/(1+.09)30}
(222222.22)x{1-.0753}
Present Value of Fund (PV) $205,473.08
c. If the rates are increasd the amount needed would decrease. An increased rate means higher returns on your investment.
d.PV
Interest Rate ( r )
Numner of periods (n)
Annunity Payment (PMT)
10%
30
-20000
Present Value of Fund (PV) $188,538.29
Formula CF=FVn/{(1+r)n-1/1}
PMT
Interest Rate ( r )
Numner of periods (n)
Future Value
PMT
10%
20
$188,538.29
($3,291.81)
188,538.29/{(1.10)20-1/.10}
1888538.29/57.274
returns on your investment.
P5-30
Year
1
2
3
4
5
A
Cash Flow
-$2,000
$3,000
$4,000
$6,000
$8,000
Present Value
Year
($1,785.71)
$2,391.58
$2,847.12
$3,813.11
$4,539.41
#########
1
2
3
4
5
6
B
Cash Flow
$10,000.00
$5,000.00
$5,000.00
$5,000.00
$5,000.00
$7,000.00
#########
Year
1
2
3
4
5
6
7
8
9
10
C
Cash Flow
$10,000
$10,000
$10,000
$10,000
$10,000
$8,000
$8,000
$8,000
$8,000
$8,000
#########
Formula PV=FVn/(1+r)n
A) PV = -2000/(1.12)^1 + 3000/(1.12)^2 + 4000/(1.12)^ 3 + 6000/(1.12)^ 4 + 8000/(1.12)^5 = $11805
B)PV = 10000/1.12^1 + 5000*(1/1.12^2 + 1/1.12^3 + 1/1.12^4 + 1/1.12^5) +7000/1.12^6 = $26034.
8000/(1.12)^5 = $11805.511
7000/1.12^6 = $26034.584
P5-36
PV
a1
5000
Time Value
Purchase answer to see full
attachment
Present Value of Expected Future Saving
Period: 2016 through 2026
Discount rate for years 2016 – 2021
Discount rate for years 2022 – 2026
Year
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
Period
1
2
3
4
5
6
7
8
9
10
11
Annual
Savings
-2000
120000
130000
150000
160000
150000
90000
90000
90000
90000
90000
=SUM(C10:C20)
PV Lump Sum
=C10/(1+$E$5)^B10
=C11/(1+$E$5)^B11
=C12/(1+$E$5)^B12
=C13/(1+$E$5)^B13
=C14/(1+$E$5)^B14
=C15/(1+$E$5)^B15
Uma Corp.
Present Value of Expected Future Savings
Period: 2016 through 2026
0.07
0.11
PV Annuity
=C16*((1-(1/(1+$E$6)^B14))/$E$6)
PV Lump Sum
=E16/(1+$E$5)^B15
Present
Value
=D10
=D11
=D12
=D13
=D14
=D15
=F16
=SUM(G10:G20)
P5-3 Future Value
PV
I
FV
###### ######
0.12
0.06
###### ######
N
6.1163 11.896
Time does not double the time but it comes close. The compounding affect on the time value of money i
Final Value = initial value(1+interest rate)time
200=100(1+0.12)n
200=100(1.0.06)n
ut it comes close. The compounding affect on the time value of money is the reason the time was not doubled.
P5-5
FV3= -1500(1.07)3Fv6=-1500(1.07)6 FV9=1500(1.07)9
a.
Future Value of a single ammount (FV)
Present Value (PV)
($1,500)
($1,500)
($1,500)
Annual Rate of Interest ( r )
7.00%
7.00%
7.00%
Number of Periods (n)
3
6
9
Future Value
b.Interest Earned FV-PV
($1,837.56)
($2,251.10)
($2,757.69)
$337.57
$413.53
$506.59
c. It is a longer period of time causing more compounded interest
P5-12
a.
PV=FV/(1+r) n
PV=6000/(1+.12)6
PV=6000/ (1.97382)
#########
They need to invest $3039.79 today to be worth $6000 in six years.
b.
PV=FV/(1+r)n
6000/(1+0.12)6
6000/(1.12)6
6000/(1.97382)
#########
c.
PV=FV/(1+r) n
PV=6000/(1+.12)6
PV=6000/ (1.97382)
#########
Each problem had the same given data, so the answers were all exactly like. The same formula was used with each
mula was used with each problem.
Time Value
P5-13
PV= FVn/(1+r)n
a.
$500/(1+0.07)3
($408.15)
b.The most he can pay is $408.15 for this payment. I would use the same formula from a to find this
c. If he invests less and still gets paid $500 three years from today, it would mean his rate of return
d mean his rate of return is higher on this ivestment.
P5-20
Amount of annuity
A
B
C
D
E
Formulas
Work
Interest rate
$12,000
$55,000
$700
$140,000
$22,500
7.00%
12.00%
20.00%
5.00%
10.00%
Ordinary Annuity Present Value
PVn=(CF/r)x[1-1/(1+r)n
a.
(12000/.07)x[1-1/(1+.07)3]
(171,428.57)x[1-1/1.225043]
171,428.57x[1-.81629]
171,428.57x.18371
$31,491.79
Annuity Due Present Value
3
PVn=(CF/r)x[1-1/(1+r)n]x(1+r) a.(12000/.07)x[1-1/(1+.07) ]x(1+.07)
(171428.57)x[1-.81629]x1.07
171428.57x.1837×1.07
$33,696.00
B Ordinary annuity is less than value of annuity due. This fact makes oridinary annuity better because the payment o
Period (years)
3
15
9
7
5
b.
PV ordinary annuity.
PV annuity due
($31,491.79)
($374,597.55)
($2,821.68)
($810,092.28)
($85,292.70)
c.
15
(55000/.12)x[1-1/(1+.12) ]
d.
9
(700/.20)x[1-1/(1+.20) ]
(458,333.33)x [1-1/(5.47)]
(3500)x[1-1/(5.15)]
458,333.33x [1-.18269]
3500x[1-.19380]
458,333.33x .8173
3500x.8062
$374,597.54
($33,696.22)
($419,549.25)
($3,386.01)
($850,596.89)
($93,821.97)
(140000/.05)x[1-1/(1+.05)7]
(2,800,000)x[1-1/1.407]
2800000x[1-.7106]
2800000x.2893
$2,821.68
$810,092.28
b.(55000/.12)x[1-1/(1+.12)15]x(1+.12)
c.(700/.20)x[1-1/(1+.20)9]x(1+.20)d.(140000/.05)x[1-1/(1+.05)7]x(1+.05)
(458333.33)x[1-.18269]x1.12
(3500)x[1-.19380]x1.2
(2800000)x[1-.71068]x1.05
458333.33x.8173×1.12
3500x.8062×1.2
2800000x.2893×1.05
$419,549.25
$3,386.01
$850,596.89
fact makes oridinary annuity better because the payment of the annuity is made at years end, whereas in annuity due the payment is made a
Difference
($2,204.43)
($44,951.71)
($564.34)
($40,504.61)
($8,529.27)
e.
(22500/.10)x[1-1/(1+.10)5]
(225,000)x[1-1/1.61]
225000x[1-.6209]
225000x.3790
$85,292.70
e.(22500/.10)x[1-1/(1+.10)5]x(1+.10)
(225,000)x[1-.6209]x(1.10)
225000x03790x1.10
$93,821.97
n annuity due the payment is made at the beginning of the year. The amount invested would be for one extra year.
P5-24
Formula PVn=(CF/r)x[1-1/(1+r)n}
a. PV
Intererst rate ( r )
Number of Periods (n)
Annuity Payment (PMT)
Present Value
b.PV
Interest Rate ( r )
Numner of periods (n)
Annunity Payment (PMT)
11% )
30
-20000
a. (-20000/.11)x{1-1/(1+.11)30}
(-181818.19)x(1-.04368)
$173,875.85
9%
30
-20000
b.(-20000/.09)x{1-1/(1+.09)30}
(222222.22)x{1-.0753}
Present Value of Fund (PV) $205,473.08
c. If the rates are increasd the amount needed would decrease. An increased rate means higher returns on your investment.
d.PV
Interest Rate ( r )
Numner of periods (n)
Annunity Payment (PMT)
10%
30
-20000
Present Value of Fund (PV) $188,538.29
Formula CF=FVn/{(1+r)n-1/1}
PMT
Interest Rate ( r )
Numner of periods (n)
Future Value
PMT
10%
20
$188,538.29
($3,291.81)
188,538.29/{(1.10)20-1/.10}
1888538.29/57.274
returns on your investment.
P5-30
Year
1
2
3
4
5
A
Cash Flow
-$2,000
$3,000
$4,000
$6,000
$8,000
Present Value
Year
($1,785.71)
$2,391.58
$2,847.12
$3,813.11
$4,539.41
#########
1
2
3
4
5
6
B
Cash Flow
$10,000.00
$5,000.00
$5,000.00
$5,000.00
$5,000.00
$7,000.00
#########
Year
1
2
3
4
5
6
7
8
9
10
C
Cash Flow
$10,000
$10,000
$10,000
$10,000
$10,000
$8,000
$8,000
$8,000
$8,000
$8,000
#########
Formula PV=FVn/(1+r)n
A) PV = -2000/(1.12)^1 + 3000/(1.12)^2 + 4000/(1.12)^ 3 + 6000/(1.12)^ 4 + 8000/(1.12)^5 = $11805
B)PV = 10000/1.12^1 + 5000*(1/1.12^2 + 1/1.12^3 + 1/1.12^4 + 1/1.12^5) +7000/1.12^6 = $26034.
8000/(1.12)^5 = $11805.511
7000/1.12^6 = $26034.584
P5-36
PV
a1
5000
Time Value
Purchase answer to see full
attachment
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