Question

Anthony wants to get a new TV. He has been working hard as a busboy at the local restaurant and wants

Answer 1

The credit card provides the opportunity for Anthony to purchase the TV by paying at a rate of $50 a month.

The correct responses are;

• 1. The final price of the TV is $791.6

• 2. Anthony has to work for 70 hours to save enough money to buy the TV

• 3. The number of extra hours of work bussing tables when using his credit card is approximately 9.16 hours.

Reasons:

The price of the TV, P = $700

The interest rate is r = 18%

The monthly payment, M = $50

Monthly payment formula is given as follows;

$M = \mathbf{ \dfrac{P \cdot \left(\dfrac{r}{12} \right) \cdot \left(1+\dfrac{r}{12} \right)^n }{\left(1+\dfrac{r}{12} \right)^n - 1}}$

The time it will take to pay using the credit card is therefore;

$\displaystyle 50 = \dfrac{700 \times \left(\dfrac{0.18}{12} \right) \cdot \left(1+\dfrac{0.18}{12} \right)^n }{\left(1+\dfrac{0.18}{12} \right)^n - 1} = \frac{10.5 \cdot 1.015^n}{1.015^n-1}$

Which gives;

50 × (1.015ⁿ - 1) = 10.5 × 1.015ⁿ

Solving for n gives;

$\displaystyle n = \frac{ln\left(\frac{50}{39.5}\right) }{ln(1.015)} \approx \mathbf{15.832}$

It will take approximately 15.832 months for Anthony to pay for the TV at $50 per month.

1. The final price of the TV = $50 × 15.832 ≈ $791.6

2. The number of hours of work, t, is given as follows;

$\displaystyle t = \frac{\ 700}{\ 10 \ per \ hour} = \mathbf{ 70 \ hours}$

Anthony has to work for 70 hours to save enough money to purchase the TV.

3. The extra hours of work is given by the hours of work needed to pay for the interest amount for the loan on the card

The interest amount on the card = $791.6 - $700 = $91.6

$\displaystyle Extra \ hours \ to \ work = \mathbf{ \frac{\ 91.6}{\ 10 \ per \ hour}} = 9.16 \ hours$

Anthony has to work for extra 9.16 hours bussing tables using his credit card.

Learn more about payment on loan here:

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