Question 335783
They want to have $10,000 by the end of 3 yhears.
They have 1500 now.
They want to make 3 equal payments at the end of each year.
The interest rate is 6% per year.


If they deposit the $1,500 today, then it will be worth 1.06^3 * 1500 = $1,786.524 in 3 years.


Subtract that from $10,000 and you get $8,213.476 that they need to provide through the 3 equal payments at the end of each year.


The amount they require for that is equal to $2,579.933409 paid into the account at the end of each year.


The yearly cash flow results for this analysis are shown below:


<pre>

time       payment	    interest on         current balance
point                       current balance
                            from previous
                            time point

0	   1500	            0	                1500
1          2579.933409      90	                4169.933409
2	   2579.933409      250.1960045	        7000.062823
3	   2579.933409      420.0037694	        10000

</pre>


To find the future value of the present amount of 1500, you use the following formula:


FUTURE VALUE OF A PRESENT AMOUNT
{{{FV(PA) = PA * (1+i)^n}}}
FV = Future Value
PA = present amount
i = Interest Rate per Time Period
n = Number of Time Periods


To find the future value of the payments of 2579.933409 at the end of each time period you use the following formula.


FUTURE VALUE OF A PAYMENT
{{{ FV(PMT) = (PMT * ((1+i)^n-1)/i) }}}
FV = Future Value
PMT = Payment per time period
i = Interest Rate per Time Period
n = Number of Time Periods


Add the two together and you should get $10,000 which is the value you wanted at the end of the 3 year time period.


In these formulas, n = 3 and i = .06