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Question 335783: Mary and Joe would like to save up $10,000 by the end of three years from now to buy new furniture for their home. They currently have $1500 in a savings account set aside for the furniture. They would like to make three equal year end deposits to this savings account to pay for the furniture when they purchase it three years from now. Assuming that this account pays 6% interest, how much should the year end payments be?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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
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