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

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