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:
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
To find the future value of the present amount of 1500, you use the following formula:
FUTURE VALUE OF A PRESENT AMOUNT
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 = 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