Question

You are planning to buy one of two brands of sofas, which you hope to use over the next twenty years. brand j costs $975 and lasts for about twenty years. brand k costs $265 and lasts for about five years, so you will need to buy four brand k sofas to equal one brand j sofa. in either case, you plan to pay for your sofa using your credit card, which has an interest rate of 14.55%, compounded monthly. you can pay off a brand j sofa with eight years of monthly payments, and you can pay off a brand k sofa with three years of monthly payments. assuming that you make no other purchases on your credit card, over twenty years, which brand will be cheaper, and how much cheaper will it be? (round all dollar values to the nearest cent.)

Answer 1

D.Brand K will be $340.32 cheaper than Brand J.

Answer 2

Using the amortization formula, sofa k will be cheaper than sofa j by $340.32

How much will each sofa cost over twenty years?

The amount each is calculated using the amortization formula:

• P = a ÷ {{[(1 + r/n)^nt] - 1} ÷ [r/n(1 + r/n)^nt]}

where:

• P is monthly payment
• a is credit amount
• r is the interest rate
• t is the time in years
• n is number of times the interest is compounded

Sofa j:

a = $975

r = 14.55% = 0.1455

t = 8 years

n = 12

P = a ÷ {{[(1 + r/n)^nt] - 1} ÷ [r/n(1 + r/n)^nt]}

P = 975 ÷ {{[(1 + 0.1455/12)^12×8] - 1} ÷ [0.1455/12(1 + 0.1455/12)^12×8]}

P = $17.24

Total amount paid = $17.24 × 96 = $1655.04

Sofa k:

a = $265

r = 14.55% = 0.1455

t = 3 years

n = 12

P = a ÷ {{[(1 + r/n)^nt] - 1} ÷ [r/n(1 + r/n)^nt]}

P = 265 ÷ {{[(1 + 0.1455/12)^12×3] - 1} ÷ [0.1455/12(1 + 0.1455/12)^12×3]}

P = $9.13

Total amount paid = $9.13 × 12 × 3 × 4 = $1314.72

Difference of amount of sofa j and sofa k = $1655.04 - $1314.72 = $340.32

Therefore, sofa k will be cheaper than sofa j by $340.32

Learn more about amortization at: https://brainly.com/question/24576997