A store sells a television for $1000. Customers can choose to receive a 10% discount and pay it off with a loan at a simple interest rate of 4%, or they can choose to pay the full price and pay it off in 3 years with no interest. if the customer plans to pay it off in 3 years, which option is better?

In order to solve this problem we must look at where to start. Since the question is asking which option is better we must compare the two options mathematically and see which one's cheaper. In order to calculate Option 1 (with the loan) we must use the Continuous Compound Interest Formula (assuming the interest compounds continually): A=Pe^rt. where "A" is the final amount, "P" is the initial cost, "r" is the interest rate by decimal, and "t" is years compounded. Because Option 1 has the incentive of 10% off, we must perform this action first; doing this makes P = 900. So now we have A = 900*e^(0.04*3), because 4% = 0.04 and it is compounded 3 years. When you compute this you will find the total balance to be $1014.75 which is more than Option 2 which costs $1000.

Jan 23rd, 2015

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