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anzhelika [568]
3 years ago
12

Bob Rohrman is offering a 2017 Toyota Camry for $29,000. If you have a 7% down payment and are able to borrow the rest at a 2.99

% APR on a 48 month loan, how much will your payments be?
Mathematics
1 answer:
Yakvenalex [24]3 years ago
6 0

Monthly installment  payment  is $597 .Total payments is $28,649

Step-by-step explanation:

Down payment = $29,000×7 ÷100= $2,030

Loan amount   =  $29,000 - 2,030 = $26,970

Interest rate     =  2.99%

Repayment period = 48 months (4 years)

simple interest formula: A = P(1 + rt) where P is the Principal amount of money to be invested at an Interest Rate R% per period for t Number of Time Periods.

= 26,970 (1+0.0299) × 4) +p =$28,648.51

= 26,970 (1+0.0299) × 4) +p =$28,648.51

Monthly payment = $596.84 (or) $597 (rounded off)

Monthly payment = $596.84 (or) $597 (rounded off)

Total payments is $28,649

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A young couple purchases their first new home in 2011 for​ $95,000. They sell it to move into a bigger home in 2018 for​ $105,00
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Given:

The value of home in 2011 is $95,000.

The value of home in 2018 is $105,000.

To find:

The exponential model for the value of the home.

Solution:

The general exponential model is

y=ab^x       ...(i)

where, a is initial value and b is growth factor.

Let 2011 is initial year and x be the number of years after 2011.

So, initial value of home is 95,000, i.e., a=95,000.

Put a=95000 in (i).

y=95000b^x       ...(ii)

The value of home in 2018 is $105,000. It means the value of y is 105000 at x=7.

105000=95000b^7

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\dfrac{21}{19}=b^7

Taking 7th root on both sides, we get

\left(\dfrac{21}{19}\right)^{\frac{1}{7}}=b

Put b=\left(\dfrac{21}{19}\right)^{\frac{1}{7}} in (ii).

y=95000\left(\left(\dfrac{21}{19}\right)^{\frac{1}{7}}\right)^x

y=95000\left(\dfrac{21}{19}\right)^{\frac{x}{7}}

Therefore, the required exponential model for the value of home is y=95000\left(\dfrac{21}{19}\right)^{\frac{x}{7}}, where x is the number of years after 2011.

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