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Thursday, 11 September 2014

Assume that in January 2010, the average house price in a particular area was $276,400. In January 2002, the average price was $193,300. What was the annual increase in selling price? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)) Annual increase in selling price % Explanation: We can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r)t Solving for r, we get: r = (FV / PV)1 / t – 1 r = ($276,400 / $193,300)1/8 – 1 = 0.0457, or 4.57% Calculator Solution: Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation. Enter 8 $193,300 ±$276,400 N I/Y PV PMT FV Solve for 4.57%

Assume that in January 2010, the average house price in a particular area was $276,400. In January 2002, the average price was $193,300.

What was the annual increase in selling price? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Annual increase in selling price

Explanation:

We can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is:

FV = PV(1 + r)^t

Solving for r, we get:

r = (FV / PV)^{1 / t} – 1

r = ($276,400 / $193,300)^1/8 – 1 = 0.0457, or 4.57%

Calculator Solution:

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

Enter

$193,300

±$276,400

I/Y

PMT

Solve for

4.57%

Solve for the unknown number of years in each of the following (Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16)): Present Value Years Interest Rate Future Value $ 510 9 % $ 1,212 760 10 1,629 17,900 17 260,563 21,000 15 391,887 Explanation: We can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r)t Solving for t, we get: t = ln(FV / PV) / ln(1 + r) FV = $1,212 = $510(1.09)t; t = ln($1,212/ $510) / ln(1.09) = 10.04 years FV = $1,629 = $760(1.10)t; t = ln($1,629/ $760) / ln(1.10) = 8.00 years FV = $260,563 = $17,900(1.17)t; t = ln($260,563 / $17,900) / ln(1.17) = 17.06 years FV = $391,887 = $21,000(1.15)t; t = ln($391,887 / $21,000) / ln(1.15) = 20.94 years Calculator Solution: Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation. Enter 9% $510 ±$1,212 N I/Y PV PMT FV Solve for 10.04 Enter 10% $760 ±$1,629 N I/Y PV PMT FV Solve for 8.00 Enter 17% $17,900 ±$260,563 N I/Y PV PMT FV Solve for 17.06 Enter 15% $21,000 ±$391,887 N I/Y PV PMT FV Solve for 20.94

Solve for the unknown number of years in each of the following (Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16)):

Present Value		Years	Interest Rate		Future Value
$	510		9	%	$	1,212
	760		10			1,629
	17,900		17			260,563
	21,000		15			391,887

Explanation:

We can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is:

FV = PV(1 + r)^t

Solving for t, we get:

t = ln(FV / PV) / ln(1 + r)

FV = $1,212 = $510(1.09)^t;	t = ln($1,212/ $510) / ln(1.09)	=	10.04 years
FV = $1,629 = $760(1.10)^t;	t = ln($1,629/ $760) / ln(1.10)	=	8.00 years
FV = $260,563 = $17,900(1.17)^t;	t = ln($260,563 / $17,900) / ln(1.17)	=	17.06 years
FV = $391,887 = $21,000(1.15)^t;	t = ln($391,887 / $21,000) / ln(1.15)	=	20.94 years

Calculator Solution:

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

Enter

$510

±$1,212

I/Y

PMT

Solve for

10.04

Enter

10%

$760

±$1,629

I/Y

PMT

Solve for

8.00

Enter

17%

$17,900

±$260,563

I/Y

PMT

Solve for

17.06

Enter

15%

$21,000

±$391,887

I/Y

PMT

Solve for

20.94

Solve for the unknown interest rate in each of the following (Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16)): Present Value Years Interest Rate Future Value $ 280 5 % $ 372 400 19 1,370 43,000 20 238,809 42,261 30 1,107,073 Explanation: We can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r)t Solving for r, we get: r = (FV / PV)1 / t – 1 FV = $372 = $280(1 + r)5; r = ($372 / $280)1/5 – 1 = 0.0585, or 5.85% FV = $1,370 = $400(1 + r)19; r = ($1,370 / $400)1/19 – 1 = 0.0669, or 6.69% FV = $238,809 = $43,000(1 + r)20; r = ($238,809 / $43,000)1/20 – 1 = 0.0895, or 8.95% FV = $1,107,073 = $42,261(1 + r)30; r = ($1,107,073 / $42,261)1/30 – 1 = 0.1150, or 11.50% Calculator Solution: Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation. Enter 5 $280 ±$372 N I/Y PV PMT FV Solve for 5.85% Enter 19 $400 ±$1,370 N I/Y PV PMT FV Solve for 6.69% Enter 20 $43,000 ±$238,809 N I/Y PV PMT FV Solve for 8.95% Enter 30 $42,261 ±$1,107,073 N I/Y PV PMT FV Solve for 11.50%

Solve for the unknown interest rate in each of the following (Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16)):

Present Value			Years	Interest Rate	Future Value
	$	280	5	%	$	372
		400	19			1,370
		43,000	20			238,809
		42,261	30			1,107,073

Explanation:

We can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is:

FV = PV(1 + r)^t

Solving for r, we get:

r = (FV / PV)^{1 / t} – 1

FV = $372 = $280(1 + r)⁵;	r = ($372 / $280)^1/5 – 1	=	0.0585, or 5.85%
FV = $1,370 = $400(1 + r)¹⁹;	r = ($1,370 / $400)^1/19 – 1	=	0.0669, or 6.69%
FV = $238,809 = $43,000(1 + r)²⁰;	r = ($238,809 / $43,000)^1/20 – 1	=	0.0895, or 8.95%
FV = $1,107,073 = $42,261(1 + r)³⁰;	r = ($1,107,073 / $42,261)^1/30 – 1	=	0.1150, or 11.50%

Calculator Solution:

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

Enter

$280

±$372

I/Y

PMT

Solve for

5.85%

Enter

$400

±$1,370

I/Y

PMT

Solve for

6.69%

Enter

$43,000

±$238,809

I/Y

PMT

Solve for

8.95%

Enter

$42,261

±$1,107,073

I/Y

PMT

Solve for

11.50%

For each of the following, compute the present value (Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16)): Present Value Years Interest Rate Future value $ 12 6 % $ 15,051 3 12 47,557 28 13 882,073 30 10 546,164 Explanation: To find the PV of a lump sum, we use: PV = FV / (1 + r)t PV = $15,051 / (1.06)12 = $ 7,479.89 PV = $47,557 / (1.12)3 = $ 33,850.13 PV = $882,073 / (1.13)28 = $ 28,794.41 PV = $546,164 / (1.10)30 = $ 31,299.87 Calculator Solution: Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation. Enter 12 6% $15,051 N I/Y PV PMT FV Solve for $7,479.89 Enter 3 12% $47,557 N I/Y PV PMT FV Solve for $33,850.13 Enter 28 13% $882,073 N I/Y PV PMT FV Solve for $28,794.41 Enter 30 10% $546,164 N I/Y PV PMT FV Solve for $31,299.87

For each of the following, compute the present value (Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16)):

Present Value	Years	Interest Rate		Future value
$	12	6	%	$	15,051
	3	12			47,557
	28	13			882,073
	30	10			546,164

Explanation:

To find the PV of a lump sum, we use:

PV = FV / (1 + r)^t

PV = $15,051 / (1.06)¹²	=	$	7,479.89
PV = $47,557 / (1.12)³	=	$	33,850.13
PV = $882,073 / (1.13)²⁸	=	$	28,794.41
PV = $546,164 / (1.10)³⁰	=	$	31,299.87

Calculator Solution:

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

Enter

$15,051

I/Y

PMT

Solve for

$7,479.89

Enter

12%

$47,557

I/Y

PMT

Solve for

$33,850.13

Enter

13%

$882,073

I/Y

PMT

Solve for

$28,794.41

Enter

10%

$546,164

I/Y

PMT

Solve for

$31,299.87

For each of the following, compute the future value (Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16)): Present Value Years Interest Rate Future Value $ 2,500 12 12 % $ 9,252 6 10 81,355 13 11 188,796 7 7 Explanation: To find the FV of a lump sum, we use: FV = PV(1 + r)t FV = $2,500(1.12)12 = $ 9,739.94 FV = $9,252(1.10)6 = $ 16,390.48 FV = $81,355(1.11)13 = $ 315,924.26 FV = $188,796(1.07)7 = $ 303,165.12 Calculator Solution: Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation. Enter 12 12% ±$2,500 N I/Y PV PMT FV Solve for $9,739.94 Enter 6 10% ±$9,252 N I/Y PV PMT FV Solve for $16,390.48 Enter 13 11% ±$81,355 N I/Y PV PMT FV Solve for $315,924.26 Enter 7 7% ±$188,796 N I/Y PV PMT FV Solve for $303,165.12

For each of the following, compute the future value (Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16)):

Present Value			Years	Interest Rate		Future Value
	$	2,500	12	12	%	$
		9,252	6	10
		81,355	13	11
		188,796	7	7

Explanation:

To find the FV of a lump sum, we use:

FV = PV(1 + r)^t

FV = $2,500(1.12)¹²	=	$	9,739.94
FV = $9,252(1.10)⁶	=	$	16,390.48
FV = $81,355(1.11)¹³	=	$	315,924.26
FV = $188,796(1.07)⁷	=	$	303,165.12

Calculator Solution:

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

Enter

12%

±$2,500

I/Y

PMT

Solve for

$9,739.94

Enter

10%

±$9,252

I/Y

PMT

Solve for

$16,390.48

Enter

11%

±$81,355

I/Y

PMT

Solve for

$315,924.26

Enter

±$188,796

I/Y

PMT

Solve for

$303,165.12