SOLUTION: Mike's Sporting Goods sells elliptical trainers under two payment plans: Under the installment plan, the customer pays $90.00 month over 5 years with interest vhanged on the balanc

Question 998243: Mike's Sporting Goods sells elliptical trainers under two payment plans: Under the installment plan, the customer pays $90.00 month over 5 years with interest vhanged on the balance at a rate of 19% year compounded monthly. Find the cash price for an elliptical trainer if it is equivalence to the price paid by a customer using the installment plan. Round your answer to two decimal places.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
f = future value
p = present value
r = interest rate per time period
n = number of time periods.
pmt = payment for each time period.
end of time period payments are assumed.

f = 0
p = what you want to find.
r = .19 / 12 = .01583333 interest rate per monthly time period.
n = 5 * 12 = 60 monthly time periods.
pmt = 90

the result is that p (present value) is equal to 3469.47.

that is the cash price you would pay that is the equivalent of the present value of 90 dollars a month for 60 months at 19% per year compounded monthly.

you can use a financial calculator, like the one below, or you can use the annuity formula and solve it manually.

using the financial calculator, you would enter the rate as a percent.

.015833333333 * 100% = 1.5833333333%

you make the required entries and then you select PV.

my entries and the results are shown below:

$$$

the manual formula you would use is:

pv = pmt * ((1 - (1 / (1 + r)^n)) / r)

using that formula you get:

pv = 90 * ((1 - (1/(1.01583333)^60)) / .01583333)

evaluate that equation and you get pv = 3469.47.

make sure you enter the parentheses in the right order and quantity.
otherwise your answer will not be the same as i got above.

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