Question

jason is looking for an engagement ring to offer his girlfriend. he has found a similar ring at each of four different jewelry stores. he doesnt have enough money to pay for the ring in cash, so he is planning on opening a line of credit (credit card) at the store he ends up buying the ring from. the chart below outlines the difference in the price of the rings the different stores offer as well as the difference in credit options. jason plans to pay off the ring purchase in 36 months. according to the information in the table, which of the jewelry stores will have the cheapest ring in the end?

a. jessies jewelry
b. über pawn
c. diamonds forever
d. drake and family gold

Explanation:

Calculate monthly payment for each store

Using the Amortized Payment Calculation and Annual Percentage Rate knowledge points

We use the amortization formula to find the monthly payment \(M\):

$$ M = P \frac{r(1+r)^n}{(1+r)^n - 1} $$

where \(n = 36\), \(r = \frac{\text{APR}}{12}\), and \(P\) is the price.

• Jessie's Jewelry: \(P = 1250\), \(r = \frac{0.19}{12} \approx 0.015833\)

$$ M = 1250 \frac{0.015833(1.015833)^{36}}{(1.015833)^{36} - 1} \approx 45.81 $$

• Über Pawn: \(P = 1328\), \(r = \frac{0.185}{12} \approx 0.015417\)

$$ M = 1328 \frac{0.015417(1.015417)^{36}}{(1.015417)^{36} - 1} \approx 48.33 $$

• Diamonds Forever: \(P = 1199\), \(r = \frac{0.21}{12} = 0.0175\)

$$ M = 1199 \frac{0.0175(1.0175)^{36}}{(1.0175)^{36} - 1} \approx 45.03 $$

• Drake and Family Gold: \(P = 1219\), \(r = \frac{0.20}{12} \approx 0.016667\)

$$ M = 1219 \frac{0.016667(1.016667)^{36}}{(1.016667)^{36} - 1} \approx 45.23 $$

Compare total cost of the ring

Using the Amortized Payment Calculation knowledge point

The total cost over 36 months is \(36 \times M\):

• Jessie's Jewelry: \(36 \times 45.81 = \$1,649.16\)
• Über Pawn: \(36 \times 48.33 = \$1,739.88\)
• Diamonds Forever: \(36 \times 45.03 = \$1,621.08\)
• Drake and Family Gold: \(36 \times 45.23 = \$1,628.28\)

Comparing these totals, Diamonds Forever offers the cheapest ring in the end.

Answer:

• a. Jessie's Jewelry
• b. Über Pawn
• c. Diamonds Forever (Correct answer)
• d. Drake and Family Gold