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Sally needs to have some drywall and insulation work done in her house. She has received a quote from a professional drywall contractor to complete her repairs for $1,200. Her neighbor Steve says he can complete the same job for $800. Sally could use a credit card to pay the contractor, but Steve can only accept cash. Sally’s credit card has a 14% APR for credit purchases and a 32% interest rate for cash advances. Expecting to pay $50 of the principle plus appropriate interest each month, Sally estimates that it would take her 24 months to pay off the contractor balance and 16 months to pay off the cash advance balance. In the end, would it be cheaper for Sally to hire the contractor or her neighbor to complete the repairs?

Respuesta :

It said the correct answer was the contractor 

Answer:

Sally can chose Steve to work with.

Step-by-step explanation:

We will calculate EMI for both the contractor and Steve.

Contractor:

EMI formula = [tex]\frac{p*r*(1+r)^{n} }{(1+r)^{n}-1 }[/tex]

p = 1200

r = 14/12/100=0.0116

n = 24

Putting values in formula we get,

[tex]\frac{1200*0.0116*(1.0116)^{24} }{(1.0116)^{24}-1 }[/tex]

= $57.62

So, for $1200 at 14% for 24 months, Sally would have to pay $57.62 per month, or 57.62*24 = $1382.88 after 24 months.

Steve:

Similarly putting these values : (p=800, r=32/12/100= 0.0266 and n=16) in above formula we get, $62.08 per month or 62.08*16= $993.28 after 16 months.

Hence, even with the higher interest rate, Sally would pay:

1382.88-993.28 = $389.60 less if she chooses to work with Steve.

Though the monthly payments are almost same for the given timelines, still Sally can chose Steve.

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