Question

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
$560		7	%	$1,389
810		8		1,821
18,400		9		289,715
21,500		11		430,258

Answer 1

Future Value:

Future Value is Value of current asset at future date grown at given int rate or growth rate.

FV = PV (1+r)^n
Where r is Int rate per period
n - No. of periods

Part A:

Particulars	Amount
Present Value	$         560.00
Future Value	$      1,389.00
Int Rate per period	7.0000%

Future Value = Cash Flow * ( 1 + r )^n
$ 1389 = $ 560 ( 1 + 0.07 ) ^ n
( 1 + 0.07 ) ^ n = $ 1389 / $ 560
1.07 ^ n = 2.4804
Take Log on Both sides
Log ( 1.07 ^ n ) = Log ( 2.4804 )
Log ( a^b ) = b * Log (a)
n * Log ( 1.07 ) = Log ( 2.4804 )
n * 0.0294 = 0.3945
n = 13.43 Years
Part B:

Particulars	Amount
Present Value	$         810.00
Future Value	$      1,821.00
Int Rate per period	8.0000%

Future Value = Cash Flow * ( 1 + r )^n
$ 1821 = $ 810 ( 1 + 0.08 ) ^ n
( 1 + 0.08 ) ^ n = $ 1821 / $ 810
1.08 ^ n = 2.2481
Take Log on Both sides
Log ( 1.08 ^ n ) = Log ( 2.2481 )
Log ( a^b ) = b * Log (a)
n * Log ( 1.08 ) = Log ( 2.2481 )
n * 0.0334 = 0.3518
n = 10.53 Years
Part C:

Particulars	Amount
Present Value	$    18,400.00
Future Value	$ 289,715.00
Int Rate per period	9.0000%

Future Value = Cash Flow * ( 1 + r )^n
$ 289715 = $ 18400 ( 1 + 0.09 ) ^ n
( 1 + 0.09 ) ^ n = $ 289715 / $ 18400
1.09 ^ n = 15.7454
Take Log on Both sides
Log ( 1.09 ^ n ) = Log ( 15.7454 )
Log ( a^b ) = b * Log (a)
n * Log ( 1.09 ) = Log ( 15.7454 )
n * 0.0374 = 1.1972
n = 31.99 Years
Part D:

Particulars	Amount
Present Value	$    21,500.00
Future Value	$ 430,258.00
Int Rate per period	11.0000%

Future Value = Cash Flow * ( 1 + r )^n
$ 430258 = $ 21500 ( 1 + 0.11 ) ^ n
( 1 + 0.11 ) ^ n = $ 430258 / $ 21500
1.11 ^ n = 20.012
Take Log on Both sides
Log ( 1.11 ^ n ) = Log ( 20.012 )
Log ( a^b ) = b * Log (a)
n * Log ( 1.11 ) = Log ( 20.012 )
n * 0.0453 = 1.3013
n = 28.71 Years