978-1259722615 Chapter 5 Solution Manual Part 3

2. The interest rate per 3 months is 6%/4 = 1.5%.

3. a. Using the annuity table, the annuity factor is 11.4699. The annual payment on the

4. The monthly payment is based on a $100,000 loan:

61.028,1$PMT000,100$

)01.1(0.01

1

0.01

1

360







 CC

5. The loan repayment is an annuity with present value equal to $4,248.68. Payments are

made monthly, and the monthly interest rate is 1%. We need to equate this expression to the

amount borrowed ($4,248.68) and solve for the number of months (t).

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Education.

2468.248,4$

)01.1(0.01

1

0.01

1

$200 



 t

t

months, or 2 years

Using a financial calculator, enter PV = ()4,248.68, FV = 0, i = 1%, PMT = 200; compute n =

24.

The effective annual rate on the loan is (1.01)12  1 = 0.1268 = 12.68%.

Est time: 06–10

Interest rates

6. r = 0.5% per month

7. EAR = e0.06  1 = 1.0618  1 = 0.0618 = 6.18%

8. a. With PV = $9,000 and FV = $10,000, the annual interest rate is determined by solving

b. With PV = $8,000 and FV = $10,000, the annual interest rate is determined by solving the

9.

a. You borrow $1,000 and repay the loan by making 12 monthly payments of $100.

b. The effective annual rate is (1.02923)12  1 = 0.41302 = 41.302%.

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Education.

10. Since the $20 initiation fee is taken out of the proceeds of the loan, the amount actually

borrowed is $1,000  $20 = $980.

11. After 1 year, each dollar invested at First National will grow to:

$1  (1.031)2 = $1.0630

12.

a. If the payment is denoted C, then:

90.202$PMT000,8$

)]12/10.0(1[)12/10.0(

1

)12/10.0(

1

48







 CC

b. The monthly interest rate is 0.10/12 = 0.008333 = 0.8333%.

13. $100  e 0.10  8 = $222.55

14.

APR Compounding

Period

Effective

Annual Rate

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Education.

a. 12% 1 month

b. 8% 3 months

c. 10% 6 months

Est time: 01–05

Simple and compound interest

15.

Effective Rate

Compounding

Period Per-Period Rate APR

a. 10.00% 1 month

b. 6.09% 6 months

1.0609(1/2)  1 =

c. 8.24% 3 months

1.0824(1/4)  1 =

Est time: 06–10

Simple and compound interest

16. APR = 1% × 52 = 52%

17. Semiannual compounding means that the 8.6% loan really carries interest of 4.3%per

half year. Similarly, the 8.4% loan has a monthly rate of 0.7%.

APR Compounding

Period Effective Annual Rate

8.6% 6 months

8.4% 1 month

1.00712  1 = 0.0873 =

18. Use trial and error to solve the following equation for r:

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Education.

%599.1000,8$

)1(

11

$240

48







 r

rrr

Using a financial calculator, enter PV = ()8,000; n = 48; PMT = 240, FV = 0; then

compute r = 1.599% per month.

APR = 1.599%  12 = 19.188%

The effective annual rate is (1.01599)12  1 = 0.2097 = 20.97%.

Est time: 06–10

Interest rates

19. According to the Rule of 72, at an interest rate of 6%, it will take 72/6 = 12 years for

your money to double. For it to quadruple, your money must double and then double again.

This will take approximately 24 years.

20. a. Using a financial calculator, solving for the r. Enter PV = 1.20; n = 4; PMT = 0, FV

= 1.41; then compute r = 4.11% per year.

b. Using a financial calculator, solving for the r. Enter PV = 0.91; n = 4; PMT = 0,

c. FV= 1.41 x (1+.0411)14=2.48

21. $80,000/(236.5/25) = $8,456.66. Her real income increased by $2,456.66.

22.

a. The real interest rate is (1.06/1.02) – 1 = 3.92%.

Education.

b. If cash flow is level in nominal terms, use the 6% nominal interest rate to discount.

23. (1 + nominal interest rate) = (1 + real interest rate)  (1 + inflation rate)

a. 1.03  1.0 = 1.03  nominal interest rate = 3.00%

24. Real interest rate =

1

rateinflation 1

rateinterest nominal 1 



25. a. $1 million will have a real value of $1 million/(1.03)50 = $228,107.

b. At a real rate of 2%, this can support a real annuity of:

950,13$PMT107,228$

)02.1(0.02

1

0.02

1

20







 CC

[To solve this on a financial calculator, enter n = 20, i = 2, PV = 228,107, FV = 0; then

compute PMT.]

Est time: 11–15

Annuities

26. (1+1.10)12 – 1 = 7,355.83 = 735.583%

27.

a. PV=

39.182,228$

)10.1(0.10

1

0.10

1

$30,000

15









b. The present value of the retirement goal is:

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Education.

c. 1.00  (1.04)30 = $3.24

d. We repeat part (a) using the real interest rate: (1.10/1.04) – 1 = 0.0577, or 5.77%.

25

1 1

PV $30,000 $530,638

0.0286 0.0286 (1.0286)

é ù

= ´ – =

ê ú

´

ë û

The real annual savings must be

50

1.0286 1 $530,808 PMT $4,902.40

0.0286

C C

 



    

 

b. If the real amount saved is $4,908.08 and prices rise at 5% per year, then the amount

saved at the end of 1 year, in nominal terms, will be:

$4,908.08  1.05 = $5,147.52

c. If the real amount saved is $4,908.08 and prices rise at 5% per year, then the amount

saved at the end of 50 year, in nominal terms, will be:

$4,908.08  (1.05)50 = $55,712.78

d. If the real amount spent is $30,000 and prices rise at 5% per year, then the amount

spent in their first year of retirement, will be:

$30,000  (1.05)50 = $344,021.99

e. If the real amount spent is $30,000 and prices rise at 5% per year, then the amount

spent in their last year of retirement, will be:

$30,000  (1.05)75 = $1,164,980.58

Est time: 16–20

Nominal and real returns

29. a. First, calculate the present value of all lifetime expenditures.

General living expenses of $50,000 per year for 50 years:

796,912$

)05.1(0.05

1

0.05

1

$50,000

50









Apartment rental of $16,000 for 8 years:

411,103$

)05.1(0.05

1

0.05

1

$16,000

8









Home purchase of $250,000 in 9 years:

PV = $250,000/(1.05)9 = $161,152

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Education.

Summing the present value of all lifetime expenditures gives $1,367,939 = 912,796 +

103,411 + 161,152 + 30,000 + 18,417 + 11,307 + 6,941 + 4,261 + 2,616 + 44,295 +

34,707 + 38,036.

Five automobile purchases of $30,000 in each of years 0, 10, 20, 30, 40, and

50:

College education of $150,000 in 25 years:

PV = $150,000/(1.0194)25 = $92,785

Summing the present value of all lifetime expenditures gives $2,433,705 = 1,591,184

To find the average salary necessary to support this lifetime consumption plan, we

solve for the 50-year payment with the same present value:

475,76$PMT705,433,2$

)0194.1(0.0194

1

0.0194

1

50







 CC

30. a. PV = $100/(1.08)3 = $79.38

b. Real value = $100/(1.03)3 = $91.51

31.

Est time: 16–20

Present value – multiple cash flows

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Education.