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PROBLEMS
Refer to 11 - Module 5 - Accounting and The Time Value of Money
FUTURE VALUE OF 1 (Problem 1, Page 7)
Case 1: PV is missing.
Assume that PV =? r = 9% n = 5 FV = 15,386. PV = FV / (1+r)n = 15,386.20 / (1.09)^5 = 15,386.20 / 1.53862 retain 5 decimal places and round off = 10, PV = FV(1+r)-n = (15,386.20)(1.09)- = (15,386.20)(0.64993) retain 5 decimal places and round off = 9,999. ≈ 10,
Case 2: r is missing.
Assume that PV = 10, r =? n = 5 FV = 15,386. r = n ⎷ (FV / PV) - 1 = 5 ⎷(15,386.20 / 10,000) - 1 = 5 ⎷1.53862 - 1
= 1.09 - 1 retain 5 decimal places and round off =. = 9%
Case 3: n is missing.
Assume that PV = 10, r = 9% n =? FV = 15,386. n = log (FV / PV) / log (1+r) = log (15,386.20 / 10,000) / log 1. = log 1.53862 / log 1. = 4.99997 retain 5 decimal places and round off ≈ 5
PRESENT VALUE OF 1 (Problem 2, Page 7)
Case 1: FV is missing.
Assume that PV = 50, r = 5% n = 14 FV =? FV = PV(1+r)n = (50,507)(1.05)^14 = (50,507)(1.97993) retain 5 decimal places and round off = 100,000. ≈ 100,
Case 2: r is missing.
Assume that PV = 50, r =? n = 14
Case 2: r is missing.
N/A
Case 3: n is missing.
Assume that R = 2, r = 8% n =? FV = 14,671. n = log { [ (FV)(r) / R ] + 1 } / log (1+r) = log { [ (14,671.84)(.08) / 2,000 ] + 1 } / log (1.08) = log [ ( 1,173.7472 / 2,000 ) + 1 ] / log (1.08) = log ( 0.58687 + 1 ) / log 1.08 retain 5 decimal places and round off = log 1.58687 / log 1. = 5.99996 retain 5 decimal places and round off ≈ 6
PRESENT VALUE OF ORDINARY ANNUITY (Problem 5, Page 9)
Case 1: R is missing.
Assume that R =? r = 10% n = 4 PV = 15,849. R = PV / { [ 1 - (1+r)-n^ ] / r} = 15,849.30 / { [ 1 - (1.1)-4^ ] / .1 } = 15,849.30 / [ ( 1 - 0.68301… ) / .1 ] = 15,849.30 / ( 0.31698… / .1 ) = 15,849.30 / 3.16987 retain 5 decimal places and round off = 4,999. ≈ 5,
Case 2: r is missing.
N/A
Case 3: n is missing.
Assume that R = 5, r = 10% n =? PV = 15,849. n = - { log { [ 1 - [ (PV)(r) / R ] } / log (1+r) } = - { log { [ 1 - [ (15,849.30)(.1) / 5,000 ] } / log (1.1) } = - { log [ 1 - ( 1,584.93 / 5,000 ) ] / log (1.1) } = - [ log ( 1 - 0.31699 ) / log (1.1) ] retain 5 decimal places and round off = - [ log 0.68301 / log (1.1) ] = -(-4.00005) retain 5 decimal places and round off = 4. ≈ 4
FUTURE VALUE OF ANNUITY DUE (Problem 6, Page 9)
Case 1: R is missing.
Assume that R =? r = 8% n = 6 FV = 15,845. R = FV / { { [ (1+r)n^ - 1 ] / r} (1+r) } = 15,845.58 / { { [ (1.08)^6 - 1 ] / .08 } (1.08) } = 15,845.58 / { [ ( 1.58687… - 1 ) / .08 ] (1.08) } = 15,845.58 / [ ( 0.58687… / .08 )(1.08) ] = 15,845.58 / [ (7.33592…)(1.08) ] = 15,845.58 / 7.92280 retain 5 decimal places and round off = 2,000 retain 5 decimal places and round off
Case 2: r is missing.
Case 3: n is missing.
Assume that R = 50, r = 12% n =? PV = 418, n = - { log { [ 1 - [ (PV)(r) / (R)(1+r) ] } / log (1+r) } = - { log { [ 1 - [ (418,289)(.12) / (50,000)(1.12) ] } / log 1.12 } = - { log [ 1 - ( 50,194.68 / 56,000 ) ] / log 1.12 } = - [ log ( 1 - 0.89633 ) / log 1.12 ] retain 5 decimal places and round off = - ( log 0.10367 / log 1.12 ) = -(-19.99972) retain 5 decimal places and round off = 19. ≈ 20
