Pearson Reviewer 10

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Centennial College *

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119

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Economics

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Feb 20, 2024

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Uploaded by JudgeNeutronBear32

Pearson Reviewer 10.2 1. What is the nominal annual rate of interest compounded quarterly at which $526.00 will accumulate to $2598.36 in eight years and three months? FV (Future Value) = 2598.36, PV (Present Value) = 526, n = 4*99/12 = 33 Formula: i= (FV/PV) ^ (1/n) – 1 i= (2598.36/526) ^(1/33) – 1 i= .049594686 * 4 = .198378747 i= 19.8379% 2. At what nominal annual rate of interest will mone y double itself in five years, six months if compounded quarterly? FV = 2, PV = 1, n =4*66/12 = 22 Formula: i= (FV/PV) ^ (1/n) – 1 I= (2/1)^(1/22) – 1 I= .032008279 * 4 = .128033118 I= 12.8033% 3. Surinder borrowed $1200.00 and agreed to pay $2384.61 in s etlement of the debt in two years, six months. What annual nominal rate compounded monthly was charged on the debt? FV = 2384.61; PV=1200; n = 12*30/12 = 30 Formula: i= (FV/PV) ^ (1/n) – 1 I = (2384.61/1200)^(1/30) – 1 I= .023154464 * 12 = .277853579 I= 27.7854% 4. Find the nominal annual rate of interest for the following investment. Principal - $1174.00; Future Value - $1773.65; Time Due- 4 years; Frequency of Conversion - quarterly FV = 1773.65; PV= 1174.00; n = 4*4 = 16 Formula: i= (FV/PV) ^ (1/n) – 1 I= (1773.65/1174)^(1/16) – 1 I= .026124339 * 4 = .104497358 I= 10.4497% 5. At what nominal rate of interest compounded quarterly will $300 earn $80 interest in six years? FV = 380; PV 300; n = 4*6 = 24  Formula = FV= PV(1+i)^n  380 = 300 (1+i)24 Redo equa�on: (380/300)^(1/24) = 1+i  9.898198713 * 100 = .9898 I= .9898%*4  I= 3.9593%

Pearson 10.3 1. What is the effec�ve annual rate of interest if $800.00 grows to $1200.00 in three years compounded quarterly? FV = 1200; PV=800, n=4*3 = 12 Formula: i= (FV/PV) ^ (1/n) – 1 I= (1200/800)^(1/12)-1 I = .034366083 F = (1+i)^m – 1 = (1+.034366083)^4 – 1 = .144714 = 14.4714% 2. What is the nominal rate of interest compounded monthly if the effec�ve rate of interest on an investment is 6.5%? R = .065 m = 12 Formula: F=(1+i)^m - 1 .065 = (1+i)^12 -1 (1+i)^12 – 1 = .065 (1+i)^12 = 1+.065  Add 1 on both sides 1+I = (1.065)^ (1/12)  divide both sides by exponent 1/12 I = .005261694  subtract 1 from both side Find the nominal rate = .005261694 * 12= 6.3140% 3. Find the nominal rate of interest compounded annually equivalent to 11.9 % compounded quarterly At one year (1+r/1)^1 = (1+.119/4)^4 ((1+r/1)^1) (1/1) = ((1+.119/4)^4) (1/1) 1+r/1 = (1+.119/4)^4  subtract 1 both sides r/1 = (1+ .119/4)^4 – 1 r = 1( (1+.119/4)^4 – 1) r = 12.4416% 4. Find the nominal annual rate of interest compounded monthly that is equivalent to 11.9% compounded quarterly (1+r/12)^12 = (1+.119/4)^4 1+r/12 = (1+.119/4)^(4/12) r/12 = (1+.119/4)^(4/12) – 1 r = 12((1+.119/4)^(4/12) – 1)  r = 11.7839%

5. (a) Find the nominal annual rate of interest at which $1500 will grow to $1800 in four years compounded monthly. (b) Find the nominal annual rate of interest at which money will double in seven years compounded quarterly. (c) Find the nominal annual rate of interest if the effec�ve annual rate of interest is 7.75% and compounding is done monthly. (d) Find the effec�ve rate of interest that is equivalent to a nominal rate of 6% compounded quarterly. a. FV (Future Value) = 1800, PV (Present Value) = 1500, n = 12*4= 48 Formula: i= (FV/PV) ^ (1/n) – 1 i= (1800/1500) ^(1/48) – 1 i= 0.0038055887 * 12 = 0.0456670644 i= 4.5667% b. FV = 2; PV = 1; n = 4*7 = 28 Formula: i= (FV/PV) ^ (1/n) – 1 I=(2/1)^(1/28)-1 I= 0.02506421196 * 4 = 0.10025684786 I = 10.0257% c. Formula: F=(1+i)^m - 1 .0 775= (1+i)^12 -1 (1+i)^12 – 1 = .0775 (1+i)^12 = 1+. 0775  Add 1 on both sides 1+I = (1. 0775)^(1/12)  divide both sides by exponent 1/12 I = 0.00623968146  subtract 1 from both side Find the nominal rate = 0.00623968146* 12= 0.07487617753 I = 7.4876% d. F = (1+.06/4)^4 -1 = 6.1364% 6. Compute the effec�ve annual rate of interest (a) for 6% compounded monthly; (b) at which $1100 will grow to $2000 in seven years compounded monthly. a. F=(1+.06/12)^12 – 1  6.1678% b. FV = 2000; PV=1100, n=12*7 = 84 Formula: i= (FV/PV) ^ (1/n) – 1 I= (2000/1100)^(1/84)-1 I = .00714249395 F = (1+i)^m – 1 F= (1+ .00714249395)^12 – 1  .08915839771  Interest Rate =8.9158%

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