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

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

  

	Present Value			Years	Interest Rate			Future Value
	$	480			9	%		$	1,111
		730			10				1,521
		17,600			17				244,409
		20,700			15				370,427

 

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)

  

0		?
–$480		$1,111

FV = $1,111 = $480(1.09)^t

t = ln($1,111 / $480) / ln(1.09)

t = 9.74 years

0		?
–$730		$1,521

FV = $1,521 = $730(1.10)^t

t = ln($1,521 / $730) / ln(1.10)

t = 7.70 years

0		?
–$17,600		$244,409

FV = $244,409 = $17,600(1.17)^t

t = ln($244,409 / $17,600) / ln(1.17)

t = 16.76 years

0		?
–$20,700		$370,427

FV = $370,427 = $20,700(1.15)^t

t = ln($370,427 / $20,700) / ln(1.15)

t = 20.64 years

Calculator Solution:

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

Enter

9%

$480

±$1,111

N

I/Y

PV

PMT

FV

Solve for

9.74

Enter

10%

$730

±$1,521

N

I/Y

PV

PMT

FV

Solve for

7.70

Enter

17%

$17,600

±$244,409

N

I/Y

PV

PMT

FV

Solve for

16.76

Enter

15%

$20,700

±$370,427

N

I/Y

PV

PMT

FV

Solve for

20.64