Question

I have looked at other answers on here in regards to this question. But I do not know what "In" stands for and those who answer are using different descriptions than I am used to. Here is the question. Number of Periods. How long will it take for $400 to grow to $1,000 at the interest rate specified? (LO1) a. 4% b. 8% c. 16%.

Could someone please break this down a little further for me.

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	$            400.00
Future Value	$         1,000.00
Int Rate per period	4.0000%

Future Value = Cash Flow * ( 1 + r )^n
$ 1000 = $ 400 ( 1 + 0.04 ) ^ n
( 1 + 0.04 ) ^ n = $ 1000 / $ 400
1.04 ^ n = 2.5
Take Log on Both sides
Log ( 1.04 ^ n ) = Log ( 2.5 )
Log ( a^b ) = b * Log (a)
n * Log ( 1.04 ) = Log ( 2.5 )
n * 0.017 = 0.3979
n = 23.3624

It took 23.36 Years

Part B:

Particulars	Amount
Present Value	$            400.00
Future Value	$         1,000.00
Int Rate per period	8.0000%

Future Value = Cash Flow * ( 1 + r )^n
$ 1000 = $ 400 ( 1 + 0.08 ) ^ n
( 1 + 0.08 ) ^ n = $ 1000 / $ 400
1.08 ^ n = 2.5
Take Log on Both sides
Log ( 1.08 ^ n ) = Log ( 2.5 )
Log ( a^b ) = b * Log (a)
n * Log ( 1.08 ) = Log ( 2.5 )
n * 0.0334 = 0.3979
n = 11.91

It took 11.91 Years

Part C:

Particulars	Amount
Present Value	$            400.00
Future Value	$         1,000.00
Int Rate per period	16.0000%

Future Value = Cash Flow * ( 1 + r )^n
$ 1000 = $ 400 ( 1 + 0.16 ) ^ n
( 1 + 0.16 ) ^ n = $ 1000 / $ 400
1.16 ^ n = 2.5
Take Log on Both sides
Log ( 1.16 ^ n ) = Log ( 2.5 )
Log ( a^b ) = b * Log (a)
n * Log ( 1.16 ) = Log ( 2.5 )
n * 0.0645 = 0.3979
n = 6.17

It took 6.17 Years.

Ln = Logarith with Base "e"

Pls comment, if any further assistance is required.