SOLUTION: A new car will cost $92,200. The dealership requires a 15% down payment. In order to save up the down payment, you set up an annuity with an annual interest rate of 4.4%. How much

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Question 1202734: A new car will cost $92,200. The dealership requires a 15% down payment. In order to save up the down payment, you set up an annuity with an annual interest rate of 4.4%. How much will you need to deposit each month in order to have the down payment in 2 years?
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Answer: $552.32


Work Shown:

15% of $92,200 = 0.15*92200 = 13,830

The down payment is $13,830

Future value of annuity formula.
FV+=+P%2A%28%281%2Bi%29%5En+-+1%29%2Fi
where,
FV = future value
P = periodic payment or deposit
i = interest rate per period (decimal form)
n = number of periods

In this case:
FV = 13830
P = unknown
i = 0.044/12 = 0.003666667 approximately
n = 12*2 = 24 months

FV+=+P%2A%28%281%2Bi%29%5En+-+1%29%2Fi

13830+=+P%2A%28%281%2B0.003666667%29%5E%2824%29+-+1%29%2F0.003666667

13830+=+P%2A25.0397432478757

P+=+13830%2F25.0397432478757

P+=+552.321957261814

P+=+552.32

You need to deposit $552.32 per month for 24 months (aka 2 years) to reach a goal of $13830.