SOLUTION: 3. You are saving to buy a car, and you deposit $250 at the end of each month for two years at an APR of 2.4% compounded monthly. What is the future value for this savings arrangem

Question 1008676: 3. You are saving to buy a car, and you deposit $250 at the end of each month for two years at an APR of 2.4% compounded monthly. What is the future value for this savings arrangement? That is, how much money will you have for the purchase of the car after two years? (Round your answer to the nearest cent.)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
250 deposited at the end of each month for 24 months at an apr of 2.4% compounded monthly will give you 6140 at the end of the 24 months.

you can use an online financial calculator to solve this.

your would enter the following:

present value = 0
future value = 0
number of time periods = 2 * 12 = 24
interest rate per time period percent = 2.4/12 = .2
pmt = -250 made at the end of each month.
the payment is shown as negative because it is money you are spending.
payment at end of time period

when you click on compute pv, it will give you the future value of 6140.

if you made the payments at the beginning of each month, then you would have 6213 at the end of the 24 months.

in order to get that, you would click on payment at beginning of time period and click on compute fv and it will give you the future value of 6152.

my results using the online calculator are shown below.

$$$

the online calculator can be found at the following link.

http://arachnoid.com/finance/index.html

there are formulas you can use to calculate this manually.

one link to a formula can be found here.

http://www.financeformulas.net/Future_Value_of_Annuity.html

this formula assumes end of period payments.

to find beginning of period payments, just multiply the result by (1+r).

the formula assumed rate per time period and numbe rof time periods.

with monthly compounding the number of time periods is 2 * 12 = 24 and the rate per time period is .025 / 12 = .002.

note that the calculator takes percent as an input but the formula takes rate as an input.

2.4% / 12 = .2% per time period for the calculator = 2.4% / 100 / 12 = .002 per time period for the formula.

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