Future Value of Varying Amounts and/or Time Intervals

The future value of multiple amounts is determined by calculating, and then adding together, the future value for each single amount. We illustrate this with Calculations #17 and #18.



Calculation #17. 
You are asked to determine the total future value on December 31, 2016 of a $1,000 deposit made on January 1, 2012 plus a $5,000 deposit made on January 1, 2014. Both amounts will earn 8% per year compounded annually. The timeline for this information is:

$1,000		$5,000			FV =	??
	←1 year→	←1 year→	←1 year→	←1 year→	←1 year→
01/01/12	12/31/12	12/31/13	12/31/14	12/31/15	12/31/16
0	1	2	3	4	5
$1,000: n = 5 years; i = 8% per year
		0	1	2	3
$5,000: n = 3 years; i = 8% per year

The total future value on December 31, 2016 is the sum of these two calculations:

Future value calculation of the $1,000 deposited on Jan 1, 2012:

FV of 1 = PV x [FV of 1 factor for n=5, i=8%]
FV of 1 = $1,000 x [1.469] ← FV factor from FV of 1 Table
FV of 1 = $1,469

Future value calculation of the $5,000 deposited on Jan 1, 2014:

FV of 1 = PV x [FV of 1 factor for n=3, i=8%]
FV of 1 = $5,000 x [1.260] ← FV factor from FV of 1 Table
FV of 1 = $6,300

The total future value on December 31, 2016 for these two deposits will be $7,769. You can verify the future value of $7,769 with the following table:

Proof of Calculation #17

Date	Interest*	Deposit	Balance
Jan 1, 2012		$1,000.00	$1,000.00
Dec 31, 2012	$ 80.00		$1,080.00
Dec 31, 2013	$ 86.40		$1,166.40
Jan 01, 2014		$5,000.00	$6,166.40
Dec 31, 2014	$493.31		$6,659.71
Dec 31, 2015	$532.78		$7,192.49
Dec 31, 2016	$575.40		$7,767.89

*8% times the previous amount appearing in the “Balance” column.

Calculation #18. 
You are asked to determine the total future value on December 31, 2016 of a $1,000 deposit made on January 1, 2012 plus a $5,000 deposit made on December 31, 2013. Both amounts will earn 8% per year compounded quarterly.

Because the interest is compounded quarterly, we convert the first deposit from 5 years to20 quarterly periods, and the second deposit from 3 years to 12 quarterly periods. We convert the interest rate of 8% per year to the rate of 2% per quarter.

The following calculations reflect the restatement to quarters. Again, the sum of the answers to these two equations will be the future value on December 31, 2016.

Future value calculation of the $1,000 deposited on Jan 1, 2012:

FV of 1 = PV x [FV of 1 factor for n=20 quarters, i=2% per quarter]
FV of 1 = $1,000 x [1.486] ← FV factor from FV of 1 Table
FV of 1 = $1,486

Future value calculation of the $5,000 deposited on Dec 31, 2013:

FV of 1 = PV x [FV of 1 factor for n=12 quarters, i=2% per quarter]
FV of 1 = $5,000 x [1.268] ← FV factor from FV of 1 Table
FV of 1 = $6,340

The total future value on December 31, 2016 for these two deposits will be $7,826. You can verify the future value of $7,826 with the following table:

Proof of Calculation #18

Date	Interest*	Deposit	Balance
Jan 1, 2012		$1,000.00	$1,000.00
Mar 31, 2012	$ 20.00		$1,020.00
Jun 30, 2012	$ 20.40		$1,040.40
Sep 30, 2012	$ 20.81		$1,061.21
Dec 31, 2012	$ 21.22		$1,082.43
Mar 31, 2013	$ 21.65		$1,104.08
Jun 30, 2013	$ 22.08		$1,126.16
Sep 30, 2013	$ 22.52		$1,148.69
Dec 31, 2013	$ 22.97	$5,000.00	$6,171.66
Mar 31, 2014	$123.43		$6,295.09
Jun 30, 2014	$125.90		$6,420.99
Sep 30, 2014	$128.42		$6,549.41
Dec 31, 2014	$130.99		$6,680.40
Mar 31, 2015	$133.61		$6,814.01
Jun 30, 2015	$136.28		$6,950.29
Sep 30, 2015	$139.01		$7,089.30
Dec 31, 2015	$141.79		$7,231.08
Mar 31, 2016	$144.62		$7,375.70
Jun 30, 2016	$147.51		$7,523.22
Sep 30, 2016	$150.46		$7,673.68
Dec 31, 2016	$153.47		$7,827.16

*2% times the previous amount appearing in the “Balance” column.