Solucionario

Chapter 4

Nominal and Effective Interest Rates

Solutions to Problems

4.1 (a) monthly (b) quarterly (c) semiannually

4.2 (a) quarterly (b) monthly (c) weekly

4.3 (a) 12 (b) 4 (c) 2

4.4 (a) 1 (b) 4 (c) 12

4.5 (a) r/semi = 0.5*2 = 1% (b) 2% (c) 4%

4.6 (a) i = 0.12/6 = 2% per two months; r/4 months = 0.02*2 = 4%

(b) r/6 months = 0.02*3 = 6%

(c) r/2 yrs = 0.02*12 = 24%

4.7 (a) 5% (b) 20%

4.8 (a) effective (b) effective (c) nominal (d) effective (e) nominal

4.9 i/6months = 0.14/2 = 7%

4.10 i = (1 + 0.04)4 – 1

= 16.99%

4.11 0.16 = (1 + r/2)2 –1

r = 15.41%

4.12 Interest rate is stated as effective. Therefore, i = 18%

4.13 0.1881 = (1 + 0.18/m)m – 1

Solve for m by trial and gives m = 2

4.14 i = (1 + 0.01)2 –1

i = 2.01%

4.15 i = 0.12/12 = 1% per month

Nominal per 6 months = 0.01(6) = 6%

Effective per 6 months = (1 + 0.06/6)6 – 1

= 6.15%

4.16 (a) i/week = 0.068/26 = 0.262%

(b) effective

4.17 PP = weekly; CP = quarterly

4.18 PP = daily; CP = quarterly

4.19 From 2% table at n =12, F/P = 1.2682

4.20 Interest rate is effective

From 6% table at n = 5, P/G = 7.9345

4.21 P = 85(P/F,2%,12) = 85(0.7885)

= $67.02 million

4.22 F = 2.7(F/P,3%,60)

= 2.7(5.8916)

= $15.91 billion

4.23 P = 5000(P/F,4%,16)

= 5000(0.5339)

= $2669.50

4.24 P = 1.2(P/F,5%,1) (in $million)

= 1.2(0.9524)

= $1,142,880

4.25 P = 1.3(P/A,1%,28)(P/F,1%,2) (in $million)

= 1.3(24.3164)(0.9803)

= $30,988,577

4.26 F = 3.9(F/P,0.5%,120) (in $billion)

= 3.9(1.8194)

= $7,095,660,000

4.27 P = 3000(250 – 150)(P/A,4%,8) (in $million)

= 3000(100)(6.7327)

= $2,019,810

4.28 F = 50(20,000,000)(F/P,1.5%,9)

= 1,000,000,000(1.1434)

= $1.1434 billion

4.29 A = 3.5(A/P,5%,12) (in $million)

= 3.5(0.11283)

= $394,905

4.30 F = 10,000(F/P,4%,4) + 25,000(F/P,4%,2) + 30,000(F/P,4%,1)

= 10,000(1.1699) + 25,000(1.0816) + 30,000(1.04)

= $69,939

4.31 i/wk = 0.25%

P = 2.99(P/A,0.25%,40)

= 2.99(38.0199)

= $113.68

4.32 i/6 mths = (1 + 0.03)2 – 1

A = 20,000(A/P,6.09%,4)

= 20,000 {[0.0609(1 + 0.0609)4]/[(1 + 0.0609)4-1]}

= 20,000(0.28919)

= $5784

4.33 F = 100,000(F/A,0.25%,8)(F/P,0.25%,3)

= 100,000(8.0704)(1.0075)

= $813,093

Subsidy = 813,093 – 800,000 = $13,093

4.34 P = (14.99 – 6.99)(P/A,1%,24)

= 8(21.2434)

= $169.95

4.35 First find P, then convert to A

P = 150,000{1 – [(1+0.20)10/(1+0.07)10}]}/(0.07 – 0.20)

= 150,000(16.5197)

= $2,477,955

A = 2,477,955(A/P,7%,10)

= 2,477,955(0.14238)

= $352,811

4.36 P = 80(P/A,3%,12) + 2(P/G,3%,12)

P = 80(9.9540) + 2(51.2482)

= $898.82

4.37 2,000,000 = A(P/A,3%,8) + 50,000(P/G,3%,8)

2,000,000 = A(7.0197) + 50,000(23.4806)

A = $117,665

4.38 P = 1000 + 2000(P/A,1.5%,12) + 3000(P/A,1.5%,16)(P/F,1.5%,12)

= 1000 + 2000(10.9075) + 3000(14.1313)(0.8364)

= $58,273

4.39 First find P in quarter –1 and then use A/P to get A in quarters 0-8.

P-1 = 1000(P/F,4%,2) + 2000(P/A,4%,2)(P/F,4%,2) + 3000(P/A,4%,4)(P/F,4%,5)

= 1000(0.9246) + 2000(1.8861)(0.9246) + 3000(3.6299)(0.8219)

= $13,363

A = 13,363(A/P,4%,9)

= 13,363(0.13449)

= $1797.19

4.40 Move deposits to end of compounding periods and then find F.

F = 1800(F/A,3%,30)

= 1800(47.5754)

= $85,636

4.41 Move withdrawals to beginning of periods and then find F.

F = (10,000 – 1000)(F/P,4%,6) – 1000(F/P,4%,5) – 1000(F/P,4%,3)

= 9000(1.2653) – 1000(1.2167) – 1000(1.1249)

= $9046

4.42 Move withdrawals to beginning of periods and deposits to end; then find F.

F = 1600(F/P,4%,5) +1400(F/P,4%,4) – 2600(F/P,4%,3) + 1000(F/P,4%,2)

-1000(F/P,4%,1)

= 1600(1.2167) + 1400(1.1699) – 2600(1.1249) + 1000(1.0816) –1000(1.04)

= $701.44

4.43 Move monthly costs to end of quarter and then find F.

Monthly costs = 495(6)(2) = $5940

End of quarter costs = 5940(3) = $17,820

F = 17,820(F/A,1.5%,4)

= 17,820(4.0909)

= $72,900

4.44 i = e0.13 – 1

= 13.88%

4.45 i = e0.12 – 1

= 12.75%

4.46 0.127 = er – 1

r/yr = 11.96%

r /quarter = 2.99%

4.47 15% per year = 15/12 = 1.25% per month

i = e0.0125 – 1 = 1.26% per month

F = 100,000(F/A,1.26%,24)

= 100,000{[1 + 0.0126)24 –1]/0.0126}

= 100,000(27.8213)

= $2,782,130

4.48 18% per year = 18/12 = 1.50% per month

i = e0.015 – 1 = 1.51% per month

P = 6000(P/A,1.51%,60)

= 6000{[(1 + 0.0151)60 – 1]/[0.0151(1 + 0.0151)60]}

= 6000(39.2792)

= $235,675

4.49 i = e0.02 – 1 = 2.02% per month

A = 50(A/P,2.02%,36)

= 50{[0.0202(1 + 0.0202)36]/[(1 + 0.0202)36 – 1]}

= 50(0.03936)

= $1,968,000

4.50 i = e0.06 – 1 = 6.18% per year

P = 85,000(P/F,6.18%,4)

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