FIN101 - Time Value of Money

8/6/2019 FIN101 - Time Value of Money

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5-1. a. FVn = PV (1 + i)n

FV10 = $5,000(1 + 0.10)10

FV10 = $5,000 (2.594)

FV10 = $12,970Or:

N = 10

I/Y = 10

PV = -5,000

PMT = 0

CPT FV = $12,969

b. FVn = PV (1 + i)n

FV7 = $8,000 (1 + 0.08)7

FV7 = $8,000 (1.714)

FV7 = $13,712

Or:

N = 7

I/Y = 8

PV = -8,000

PMT = 0CPT FV = $13,711



c. FV12 = PV (1 + i)n

FV12 = $775 (1 + 0.12)12

FV12 = $775 (3.896)

FV12 = $3,019.40Or:

N = 12

I/Y = 12

PV = -775

PMT = 0

CPT FV = $3,019

d. FVn = PV (1 + i)n

FV5 = $21,000 (1 + 0.05)5

FV5 = $21,000 (1.276)

FV5 = $26,796.00

Or:

N = 5

I/Y = 5

PV = -21,000

PMT = 0CPT FV = $26,802. (this is the correct answer, notice the slight

rounding error when the tables were used above)

5-2. a. FVn = PV (1 + i)n

$1,039.50 = $500 (1 + 0.05)n

2.079 = FVIF 5%, n yr.

Thus n = 15 years (because the value of 2.079 occurs in the 15-year row of the 5% column of Appendix B).

Or:

I/Y = 5

PV = -500,000

PMT = 0

FV = 1,039.50



CPT N = 15




$53.87 = $35 (1 + .09)n

1.539 = FVIF 9%, n yr.

Thus, n = 5 yearsOr:

I/Y = 9

PV = -35.0

PMT = 0

FV = 53.87

CPT N = 5

c. FVn = PV (1 + i)n

$298.60 = $100 (1 + 0.2)n 2.986 = FVIF 20%, n yr.

Thus, n = 6 years

Or:

I/Y = 20

PV = -100.0

PMT = 0

FV = 298.60

CPT N = 6


$78.76 = $53 (1 + 0.02)n

1.486 = FVIF 2%, n yr.

Thus, n = 20 years

Or:

I/Y = 2

PV = -53.0

PMT = 0FV = 78.76

CPT N = 20



5-3. a. FVn = PV (1 + i)n

$1,948 = $500 (1 + i)12

3.896 = FVIF i%, 12 yr.

Thus, i = 12% (because the Appendix B value of 3.896 occurs in the 12-year row in the 12% column)

Or:

N = 12

CPT I/Y = 12

PV = -500

PMT = 0

FV = 1,948

b. FVn

= PV (1 + i)n

$422.10 = $300 (1 + i)7

1.407 = FVIF i%, 7 yr.

Thus, i = 5%

Or:

N = 7

CPT I/Y = 4.999

PV = -300

PMT = 0

FV = 422.10


$280.20 = $50 ( 1 + i)20

5.604 = FVIF i%, 20 yr.

Thus, i = 9%

Or:

N = 20

CPT I/Y = 9PV = -50

PMT = 0

FV = 280.20



d. FVn = PV ( 1 + i)n

$497.60 = $200 (1 + i)5

00.200$

60.497$= FVIF i%, 5 yr.

Thus, i = 20%

Or:

N = 5

CPT I/Y = 20

PV = -200

PMT = 0

FV = 497.60

5-4. a. PV = FVn ( )

+ ni 1

1

PV = $800( )

+ 100.1 1

1

PV = $800 (0.386)

PV = $308.80

Or:

N = 10

I/Y = 10

CPT PV = -308.43

PMT = 0

FV = 800

b. PV = FVn ( )

+ ni 1

1

PV = $300 ( )

+ 505.0 1

1

PV = $300 (0.784)

PV = $235.20



Or:

N = 5

I/Y = 5

CPT PV = -235.06

PMT = 0FV = 300

c. PV = FVn

( )

+ ni 1

1

PV = $1,000( )

+ 803.0 1

1

PV = $1,000 (0.789)

PV = $789Or:

N = 8

I/Y = 3

CPT PV = -789

PMT = 0

FV = 1,000

d. PV = FVn ( )

+ ni 1

1

PV = $1,000( )

+ 82.0 1

1

PV = $1,000 (0.233)

PV = $233

Or:

N = 8

I/Y = 20CPT PV = -233

PMT = 0

FV = 1,000



5-5. a. FVn = PMT ( )

+∑

−

=

1n

0t

ti 1

FV = $500 ( )

+

∑

−

=

110

0t

t0.05 1

FV10 = $500 (12.578)

FV10 = $6,289

Or:

N = 10

I/Y = 5

PV = 0

PMT = -500

CPT FV = 6,289

b. FVn = PMT ( )

+∑

−

=

1n

0t

ti 1

FV5 = $100 ( )

+∑

−

=

15

0t

t1.0 1

FV5 = $100 (6.105)

FV5 = $610.50

Or:

N = 5

I/Y = 10

PV = 0

PMT = -100

CPT FV = 610.51

c. FVn = PMT ( )

+∑

−

=

17

0t

ti 1

FV7 = $35 ( )

+∑

−

=

17

0t

t0.07 1

FV7 = $35 (8.654)

FV7 = $302.89



Or:

N = 7

I/Y = 7

PV = 0

PMT = -35CPT FV = 302.89

d. FVn = PMT ( )

+∑

−

=

1n

0t

ti 1

FV3 = $25 ( )

+∑

−

=

13

0t

t0.02 1

FV3 = $25 (3.060)

FV3 = $76.50

Or:

N = 3

I/Y = 2

PV = 0

PMT = -25

CPT FV = 76.51

5-6. a. PV = PMT( )

+∑=

n

1tt

i 1

1

PV = $2,500( )

+∑=

10

1tt

07.0 1

1

PV = $2,500 (7.024)

PV = $17,560

Or:

N = 10

I/Y = 7CPT PV = 17,559

PMT = -2,500

FV = 0



b. PV = PMT( )

+∑=

n

1tt

i 1

1

PV = $70 ( )

+∑=

3

1tt03.0 1

1

PV = $70 (2.829)

PV = $198.03

Or:

N = 3

I/Y = 3

CPT PV = -198

PMT = 70

FV = 0

c. PV = PMT( )

+∑=

n

1tt

i 1

1

PV = $280( )

+∑=

7

1tt

0.06 1

1

PV = $280 (5.582)

PV = $1,562.96

Or: N = 7

I/Y = 6

CPT PV = -1,563.06

PMT = 280

FV = 0

d. PV = PMT( )

+∑=

n

1t

ti 1

1

PV = $500( )

+∑=

10

1tt

0.1 1

1

PV = $500 (6.145)

PV = $3,072.50



Or:

N = 10

I/Y = 10

CPT PV = -3,072.28

PMT = 500FV = 0

5-7. a. FVn = PV (1 + i)n

compounded for 1 year

FV1 = $10,000 (1 + 0.06)1

FV1 = $10,000 (1.06)

FV1 = $10,600

Or: N = 1

I/Y = 6

PV = -10,000

PMT = 0

CPT FV = $10,600

compounded for 5 years

FV5 = $10,000 (1 + 0.06)5

FV5 = $10,000 (1.338)FV5 = $13,380

Or:

N = 5

I/Y = 6

PV = -10,000

PMT = 0

CPT FV = $13,382

compounded for 15 years

FV15 = $10,000 (1 + 0.06)15

FV15 = $10,000 (2.397)

FV15 = $23,970



Or:

N = 15

I/Y = 6

PV = -10,000

PMT = 0CPT FV = $23,966


compounded for 1 year at 8%

FV1 = $10,000 (1 + 0.08)1

FV1 = $10,000 (1.080)

FV1 = $10,800

Or: N = 1

I/Y = 8

PV = -10,000

PMT = 0

CPT FV = $10,800

compounded for 5 years at 8%

FV5 = $10,000 (1 + 0.08)5

FV5 = $10,000 (1.469)

FV5 = $14,690

Or:

N = 5

I/Y = 8

PV = -10,000

PMT = 0

CPT FV = $14,693


FV15 = $10,000 (1 + 0.08)15

FV15 = $10,000 (3.172)

FV15 = $31,720



Or:

N = 15

I/Y = 8

PV = -10,000

PMT = 0CPT FV = $31,722

compounded for 1 year at 10%

FV1 = $10,000 (1 + 0.1)1

FV1 = $10,000 (1 + 1.100)

FV1 = $11,000

Or:

N = 1

I/Y = 10

PV = -10,000

PMT = 0

CPT FV = $11,000


FV5 = $10,000 (1 + 0.1)5

FV5 = $10,000 (1.611)

FV5 = $16,110Or:

N = 5

I/Y = 10

PV = -10,000

PMT = 0

CPT FV = $16,105


FV15 = $10,000 (1 + 0.1)15

FV15 = $10,000 (4.177)

FV15 = $41,770



Or:

N = 15

I/Y = 10

PV = -10,000

PMT = 0CPT FV = $41,772

c. There is a positive relationship between both the interest rate used to compound a present sum and the number of years for which the compounding continues andthe future value of that sum.

5-8. FVn = PV (1 +m

i)mn

Account PV i m n (1 + )mn

PV(1 + )mn

Theodore Logan III $ 1,000 10% 1 10 2.594 $ 2,594Vernell Coles 95,000 12 12 1 1.127 107,065Thomas Elliott 8,000 12 6 2 1.268 10,144Wayne Robinson 120,000 8 4 2 1.172 140,640Eugene Chung 30,000 10 2 4 1.477 44,310Kelly Cravens 15,000 12 3 3 1.423 21,345

5-9. a. FVn = PV (1 + i)n

FV5 = $5,000 (1 + 0.06)5

FV5 = $5,000 (1.338)

FV5 = $6,690

Or:

N = 5

I/Y = 6

PV = -5,000

PMT = 0

CPT FV = $6,691

b. FVn = PV (1 + )mn

FV5 = $5,000 (1 + )2X5

FV5 = $5,000 (1 + 0.03)10

FV5 = $5,000 (1.344)

FV5 = $6,720

Or:



Using a financial calculator where you can change the number of times compoundingoccurs per year, you can solve this problem in one of two ways.

One way to solve this problem if you’re using a Texas Instruments BAII-Plus calculator is to first make P/Y = 2

N = 5 X 2 = 10I/Y = 6

PV = -5,000

PMT = 0

CPT FV = $6,720

OR if you don’t want to use P/Y button (that is, set P/Y=1)

N = 5 X 2 = 10

I/Y = 6/2

PV = -24

PMT = 0

CPT FV = $6,720

Now solving for bimonthly compounding (six times per year):

FVn = PV (1 + )mn

FV5 = $5,000 (1 + )6X5

FV5 = $5,000 (1 + 0.01)30

FV5 = $5,000 (1.348)FV5 = $6,740



N = 5 X 6 = 30

I/Y = 6

PV = -5,000

PMT = 0

CPT FV = $6,739




N = 5 X 6 = 30

I/Y = 6/6

PV = -5,000

PMT = 0

CPT FV = $6,739


FV5 = $5,000 (1 + 0.12)5

FV5 = $5,000 (1.762)

FV5 = $8,810

Or:

N = 5

I/Y = 12

PV = -5,000

PMT = 0

CPT FV = $8,812

FV5 = PVmn

m

i 1

+

FV5 = $5,000 +

2

12.0 1 2X5

FV5 = $5,000 (1 + 0.06)10

FV5 = $5,000 (1.791)

FV5 = $8,955

Or:






FV12 = $5,000 (1 + 0.06)12

FV12 = $5,000 (2.012)

FV12 = $10,060Or:

N = 12

I/Y = 6

PV = -5,000

PMT = 0

CPT FV =$10,061

e. An increase in the stated interest rate will increase the future value of a givensum. Likewise, an increase in the length of the holding period will increase the

future value of a given sum.

5-10. Annuity A: PV = PMT( )

+∑=

n

1tt

i 1

1

PV = $8,500( )

+∑=

12

1tt

0.11 1

1

PV = $8,500 (6.492)

PV = $55,182

OR:

N = 12

I/Y = 11

CPT PV = -$55,185

PMT = -8,500

FV = 0

Since the cost of this annuity is $50,000 and its present value is $55,182,given an 11% opportunity cost, this annuity has value and should beaccepted.



Annuity B: PV = PMT( )

+∑=

n

1tt

i 1

1

PV = $7,000

( )

+∑=

25

1t t0.11 1

1

PV = $7,000 (8.422)

PV = $58,954

OR:

N = 25

I/Y = 11

CPT PV = -$58,952

PMT = -7,000

FV = 0

Since the cost of this annuity is $60,000 and its present value is only$58,954, given an 11% opportunity cost, this annuity should not beaccepted.

Annuity C: PV = PMT( )

+∑=

n

1tt

i 1

1

PV = $8,000( )

+∑=

20

1tt

0.11 1

1

PV = $8,000 (7.963)

PV = $63,704

OR:

N = 20

I/Y = 11

CPT PV = -$63,707

PMT = -8,000

FV = 0

Since the cost of this annuity is $70,000 and its present value is only$63,704, given an 11% opportunity cost, this annuity should not beaccepted.



5-11. Year 1: FVn = PV (1 + i)n

FV1 = 15,000 (1 + 0.2)1

FV1 = 15,000 (1.200)

FV1 = 18,000 books

OR:

N = 1

I/Y = 20

PV = -15,000

PMT = 0

CPT FV = 18,000 books

Year 2: FVn = PV (1 + i)n

FV 2 = 15,000 (1 + 0.2)2

FV 2 = 15,000 (1.440)

FV2 = 21,600 books

OR:

N = 2

I/Y = 20

PV = -15,000

PMT = 0


Year 3: FVn = PV (1 + i)n

FV3 = 15,000 (1.20)3

FV3 = 15,000 (1.728)

FV3 = 25,920 books

OR:

N = 3

I/Y = 20PV = -15,000

PMT = 0




Book sales

25,000

20,000

15,000

1 2 3

years

The sales trend graph is not linear, because this is a compound growth trend. Just ascompound interest occurs when interest paid on the investment during the first period isadded to the principal of the second period, interest is earned on the new sum. Book sales growth was compounded; thus, the first year the growth was 20% of 15,000 books,the second year 20% of 18,000 books, and the third year 20% of 21,600 books.

5-12. FVn = PV (1 + i)n

FV1 = 73(1 + 0.10)1

FV1 = 73(1.10)

FV1 = 80.3 Home Runs in 2002

OR:

N = 1

I/Y = 10

PV = -73

PMT = 0

CPT FV = 80.3 home runs



FV2 = 73(1 + 0.10)2

FV2 = 73(1.21)

FV2 = 88.33 Home Runs in 2003

OR:

N = 2

I/Y = 10

PV = -73

PMT = 0


FV3 = 73(1 + 0.10)3

FV3 = 73(1.331)

FV3 = 97.163 Home Runs in 2004.

OR:

N = 3

I/Y = 10

PV = -73

PMT = 0


FV3 = 73(1 + 0.10)4

FV4 = 73(1.464)

FV4 = 106.87 Home Runs in 2005.

OR:

N = 4

I/Y = 10

PV = -73PMT = 0




FV5 = 73(1 + 0.10)5

FV5 = 73(1.611)

FV5 = 117.5672 Home Runs in 2006.

OR:

N = 5

I/Y = 10

PV = -73

PMT = 0


5-13. PV = PMT( )

+∑=

n

1tt

i 1

1

$60,000 = PMT( )

+

∑=

25

1tt

0.09 1

1

$60,000 = PMT (9.823)

Thus, PMT = $6,108.11 per year for 25 years.

OR:

N = 25

I/Y = 9

PV = 60,000

CPT PMT= -$6,108.38

FV = 0

5-14. FVn = PMT ( )

+∑

−

=

1n

0t

ti 1

$15,000 = PMT ( )

+∑

−

=

115

0t

t0.06 1

$15,000 = PMT (23.276)

Thus, PMT = $644.44



5-18. One dollar at 12.0% compounded monthly for one year

FVn = PV (1 + 1)n

FV12 = $1(1 + .01)12

= $1(1.127)

= $1.127



N = 1 X 12 = 12

I/Y = 12

PV = -1PMT = 0

CPT FV = $1.1268


N = 1 X 12 = 12

I/Y = 12/12

PV = -1

PMT = 0

CPT FV = $1.1268

One dollar at 13.0% compounded annually for one year

FVn = PV (1 + i)n

FV1 = $1(1 + .13)1

= $1(1.13)

= $1.13

OR

N = 1

I/Y = 13

PV = -1

PMT = 0

CPT FV = $1.13

The loan at 12% compounded monthly is more attractive.



5-19. Investment A

PV = PMT( )

+∑=

n

1tt

i 1

1

= $10,000( )

+∑=

5

1tt

.20 1

1

= $10,000(2.991)

= $29,910

OR:

N = 5

I/Y = 20

CPT PV = -29,906

PMT = 10,000

FV = 0

Investment B

Step 1: First, discount the annuity back to the beginning of year 5, which is the end of year 4.Then, discount this equivalent sum to present.

PV = PMT( )

+∑=

n

1tt

i 1

1

= $10,000( )

+∑=

6

1tt

.20 1

1

= $10,000(3.326)

= $33,260—then discount the equivalent sum

back to present.

Or: Step 1:

N = 6

I/Y = 20

CPT PV = -33,255

PMT = 10,000

FV = 0

Step 2:



PV = FVn ( )

+ ni 1

1

= $33,260

+ 4)20.1(

1

= $33,260(.482)

= $16,031.32

Or: Step 2:

N = 4

I/Y = 20

CPT PV = 16,037

PMT = 0

FV = -33,255

Investment C

PV = FVn

+ ni) (1

1

= $10,000

+ 1)20. 1(

1+ $50,000

+ 6)20. 1(

1

+ $10,000

+ 10)20. 1(

1

= $10,000(.833) + $50,000(.335) + $10,000(.162)

= $8,330 + $16,750 + $1,620

= $26,700

OR: Simply calculate the present value of all three single cash flows and then add themtogether:

N = 1

I/Y = 20

CPT PV = 8,333

PMT = 0

FV = 10,000



b. PV =i

PP

PV =12.0

000,1$

PV = $8,333.33

c. PV =i

PP

PV =09.0

100$

PV = $1,111.11

d. PV =i

PP

PV =05.0

95$

PV = $1,900

5-22. FVn = PV

nxm

m

i 1

+

4 = 1nx2

2

0.16 1

+

4 = (1 + 0.08)2 x n

4 = FVIF8%, 2n yr.

A value of 3.996 occurs in the 8% column and 18-year row of the table inAppendix B. Therefore, 2n = 18 years and n = approximately 9 years.

OR:

Using a financial calculator where you can change the number of timescompounding occurs per year, you can solve this problem in one of two ways.

One way to solve this problem if you’re using a Texas Instruments BAII-Pluscalculator is to first make P/Y = 2

CPT N = 18 and since P/Y = 2, there are two periods per year, so

N = 9 years

I/Y = 16

PV = -1

PMT = 0

FV = 4




CPT N = 18 and since the interest rate is expressed in semi-annual

terms, there are two periods per year, so N=9 years

I/Y = 16/2

PV = -1

PMT = 0

FV = 4

5-23. The present value of the $10,000 annuity over years 11-15.

PV = PMT( ) ( )

+

+∑∑==

10

1tt

15

1tt

.06 1

1 -

.06 1

1

= $10,000(9.712 - 7.360)

= $10,000(2.352)

= $23,520

Alternatively, you could first bring the 5 year $10,000 annuity back to the beginning of year 11, which is the same as the end of year 10. In effect, you haveconsolidated the five year annuity into a single cash flow at the end of year 10,then bring that equivalent cash flow back to present:

The present value of the $20,000 withdrawal at the end of year 15:

PV = FV15

+ 15

)06.1(

1

= $20,000(.417)

= $8,340

Thus, you would have to deposit $23,520 + $8,340 or $31,860 today.

OR:

Step 1: First, discount the annuity back to the beginning of year 11, which is the end

of year 10. Then, discount this equivalent sum to present.



PV = PMT( )

+∑=

n

1tt

i 1

1

= $10,000 ( )

+∑=5

1tt.06 1

1

= $10,000(4.212)

= $42,120 — then discount the equivalent sum

back to present.

Step 2: Then discount the $42,120 back to present:

PV = FVn

+ ni) (1

1

PV = $42,120

+ 10)06. 1(

1

PV = $42,120 (.558)

PV = $23,503

Then add the present value of the $20,000 withdrawal at the end of year 15 to this amount:

PV = FV15

+ 15

)06.1(

1

= $20,000(.417)

= $8,340


Or: Step 1 (First, discount the annuity back to the beginning of year 11, which is the end of year 10.):

N = 5

I/Y = 6

CPT PV = -42,124

PMT = 10,000FV = 0



Step 2 (Then, discount this equivalent sum to present.):

N = 10

I/Y = 6

CPT PV = 23,473

PMT = 0FV = -42,124

Step 3 (Then, determine the present value of the $20,000 withdrawal at the end of year 15):

N = 15

I/Y = 6

CPT PV = 8,345

PMT = 0

FV = -20,000

Step 4: (Add the present values together):


5-24. PV = PMT( )

+∑=

10

1tt

.10 1

1

$40,000 = PMT (6.145)

PMT = $6,509.36OR:

N = 10

I/Y = 10

PV = -40,000

CPT PMT= $6,510

FV = 0

5-25. PV = PMT( )

+∑=

5

1tt

i 1

1

$30,000 = $10,000 (PVIFAi%, 5 yr.)

3.0 = PVIFAi%, 5 yr.

i = 19.86%



OR:

N = 5

CPT I/Y = 19.86%

PV = -30,000

PMT = 10,000

FV = 0

5-26. PV = FVn

+ ni) (1

1

$10,000 = $27,027 (PVIFi%, 5 yr.)

.370 = PVIFi%, 5 yr.

Thus, i = 22%

OR:

N = 5

CPT I/Y = 22.0%

PV = -10,000

PMT = 0

FV = 27,027

5-27. PV = PMT ( )

+∑=

n

1tti 1

1

$25,000 = PMT( )

+∑=

5

1t12. 1

1

$25,000 = PMT (3.605)

PMT = $6,934.81OR:

N = 5

I/Y = 12

PV = -25,000

CPT PMT = $6,935

FV = 0



5-28. The present value of $10,000 in 12 years at 11 percent is:

PV = FVn

+ ti) (1

1

PV = $10,000

+ 12.11) (1

1

PV = $10,000 (.286)

PV = $2,860

OR:

N = 12

I/Y = 11

CPT PV = 2,858

PMT = 0

FV = -10,000

The present value of $25,000 in 25 years at 11% is:

PV = $25,000

+ 25.11) (1

1

= $25,000 (.074)

= $1,850

Thus, take the $10,000 in 12 years.

OR:

N = 25

I/Y = 11

CPT PV = 8,345

PMT = 0

FV = -1,840

5-29. FVn = PMT ( )

+∑

−

=

1n

0t

ti 1

$20,000 = PMT ( )

+

∑

−

=

15

0t

t.12 1

$20,000 = PMT(6.353)

PMT = $3,148.12



OR: If you solve this problem if you’re using a Texas Instruments BAII-Plus calculator you can use the P/Y function and make P/Y = 12:

N = 5 X 12 = 60

I/Y = 6.2

PV = -25,000

CPT PMT = 485.65

FV = 0

5-46. Since this problem involves monthly payments there are two ways to solve it:


N = 36

CPT I/Y = 11.62

PV = -999

PMT = 33

FV = 0


N = 36

CPT I/Y = 0.9683 X 12 =11.62% (remember, we just calculated the

monthly interest rate because n was expressed in months, so to calculate the

annual rate we multiply it times 12)

PV = -999

PMT = 33

FV = 0

5-47. First, what will be the monthly payments if Suzie goes for the 4.9 percent financing?Since this problem involves monthly payments there are two ways to solve it:


N = 60

I/Y = 4.9

PV = -25,000

CPT PMT= $470.64

FV = 0



b. The future value of the $20,000 is:

N = 15 X 4 = 60

I/Y = 9/4

PV = -20,000

PMT = 0

CPT FV = $76,003

OR if you want to use P/Y button (that is, set P/Y=4)

N = 15 X 4 = 60

I/Y = 9

PV = -20,000

PMT = 0

CPT FV = $76,003

Adding the present values together: $287,138 + $76,003 = $363,141.

5-52. N = 20

CPT I/Y = 13%

PV = -21,074.25

PMT = 3,000

FV = 0

5-53. First, let’s figure out how much he will need at age 65 to receive $80,000 each year for 15 years:

N = 15

I/Y = 6

CPT PV = -776,980

PMT = 80,000

FV = 0

In addition to receiving $80,000 each year for 15 years, Milhouse wants to receive$300,000 at age 65 (in 43 years). How much must he deposit at the end of eachyear to end up with $300,000 + $776,980 = $1,076,980 in 43 years if he earns 9%

on his money: N = 43

I/Y = 9

PV = 0

CPT PMT = -2,442.99

FV = 1,076,980



SOLUTION TO MINI CASE

a. Discounting is the inverse of compounding. We really have only one formula to move asingle cash flow through time. In some instances, we are interested in bringing that cashflow back to the present (finding its present value) when we already know the futurevalue. In other cases, we are merely solving for the future value where we know the present value.

b. The values in the present value of an annuity table (Table 5-8) are actually derived fromthe values in the present value table (Table 5-4). This can be seen by examining thevalue represented in each table. The present value table gives values of

ni) (1

1

+

for various values of i and n, while the present value of an annuity table gives values of

( )

+∑=

n

1tt

i 1

1

for various values of i and n. Thus, the value in the present value of annuity for an n-year annuity for any discount rate i is merely the sum of the first n value in the present valuetable.

c. (1) FVn = PV (1 + i)n

FV11 = $5,000(1 + 0.08)10

FV11 = $5,000 (2.159)

FV11 = $10,795

OR:

N = 10

I/Y = 8

PV = -5,000

PMT = 0

CPT FV = $10,795

(2) FVn = PV (1 + i)n

$1,671 = $400 (1 + 0.10)n

4.1775 = FVIF10%, n yr.

Thus, n = 15 years (because the value of 4.177 occurs in the 15 year row of the 10% column of Appendix B).




N = 10

I/Y = 10/2

PV = -1,000

PMT = 0

CPT FV = 1,629

e. An annuity due is an annuity in which the payments occur at the beginning of each periodas opposed to occurring at the end of each period, which is when the payment occurs inan ordinary annuity.

f. PV = PMT(PVIFAi,n)

= $1,000(PVIFA10%, 7 yrs.)

= $1,000(4.868)

= $4,868

OR:

N = 7

I/Y = 10

CPT PV = -4,868

PMT = 1,000

FV = 0

PV(annuity due) = PMT(PVIFAi,n

)(l+i)

= $1000(4.868)(l+.10)

= $5,354.80

OR:

N = 7

I/Y = 10

CPT PV = -4,868 X 1.1 = 5,355

PMT = 1,000

FV = 0

g. FV = PMT(FVIFAi,n)

= $1,000(9.487)

= $9,487



OR:

N = 7

I/Y = 10

PV = 0

PMT = -1,000

CPT FV = 9,487

FVn(annuity due) = PMT(FVIFAi,n)(l+i)

= $1000(9.487)(l+.10)

= $10,435.70

OR:

N = 7

I/Y = 10

PV = 0

PMT = -1,000

CPT FV = 9,487 X 1.1 = 10,436

h. PV = PMT(PVIFAi,n)

$100,000 = PMT(PVIFA10%, 25 yrs.)

$100,000 = PMT(9.077)

$11,016.86 = PMT

OR:

N = 25

I/Y = 10

PV = -100,000

CPT PMT= 11,017

FV = 0

i. PV =i

PP

=08.

000,1$

= $12,500

FIN101 - Time Value of Money

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