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# Solve the problem. Round monetary amounts to the nearest cent. Adam bought a $1,670 custom video game/sound system on a special no-interest plan. He made a$100 down payment and agreed to pay the entire purchase off in$1\frac{1}{2}$years. The minimum monthly payment is $10. If he makes the minimum monthly payment up until the last payment, what will be the amount of his last payment? Solution Verified Step 1 1 of 2 Given: Purchase price=$1,670

Down payment=$100 Monthly payment=$10

Number of months (excluding 18th month)=17

The total amount of monthly payments is the product of the number of months and the monthly payment.

\begin{align*} \text{Total amount of monthly payments}&=\text{Number of months}\times \text{Monthly payment} \\ &=17\times 10 \\ &=170 \end{align*}

The total cost is the sum of the down payment and the total amount of monthly payments:

\begin{align*} \text{Total cost}&=\text{Total amount of monthly payments}+\text{Down payment} \\ &=170+100 \\ &=270 \end{align*}

The remaining payment is then the difference between the purchase price and the total cost (of the first 17 months), as there is no interest in this case and thus only the remaining amount of the purchase price should still have to be paid:

\begin{align*} \text{Remaining payment}&=\text{Purchase price}-\text{Total cost} \\ &=1670-270 \\ &=1400 \end{align*}

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