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Nellie has a bankruptcy on her credit report and therefore pays higher interest rates on her current loans. She took out a car loan for $45,000 payable for 6 years at an interest rate of 15%. If she had not applied for bankruptcy, she would have been able to take out the loan at a rate of 6%. Approximately how much more in interest over the life of the loan does Nellie have to pay? a. $68,510.16 b. $53,696.16 c. $32,206.32 d. $14,814.00

Respuesta :

Using simple interest, it is found that she has to pay $24,300 more in interest.

The amount of money after t years, in simple interest, is given by:

[tex]A(t) = P(1 + kt)[/tex]

In which:

  • P is the principal.
  • k is the interest rate, as a decimal.
  • t is the time, in years.

In this problem:

  • Loan of $45,000, thus [tex]P = 45000[/tex].
  • 6 years, thus [tex]t = 6[/tex].

The amount with 15% interest is:

Here, [tex]k = 0.15[/tex]

[tex]A(6) = 45000[1 + 0.15(6)] = 85,500[/tex]

The amount with 6% interest is:

Here [tex]k = 0.06[/tex].

[tex]A(6) = 45000[1 + 0.06(6)] = 61,200[/tex]

The difference is:

85,500 - 61,200 = 24,300

She has to pay $24,300 more in interest.

A similar problem is given at https://brainly.com/question/24989537

cranejohnathan

Answer:

I cracked the code on my journey to find the correct answer to this problem

The answer is D or $14,814.00

Step-by-step explanation:

This is more than simple interest, this is something to do with amortization

this is a monthly payment calculator for a car loan

[tex]A=p\cdot\frac{\left(r\left(r+1\right)^{n}\right)}{\left(\left(1+r\right)^{n}-1\right)}\\[/tex]

This isn't exactly what we are looking for since we aren't looking for monthly payments but this can still help.

So our variables are [tex]p=45,000[/tex], where p is for principle

r is the loan rate in monthly terms or divide the interest by 12 which is [tex]r=0.0125[/tex] for when 15% is interest and [tex]r=0.0005[/tex] when 6% is interest.

and n is years times 12 or monthly periods involved so [tex]n=72[/tex]

so our equation is [tex]45000\cdot\frac{\left(0.00125\left(0.00125+1\right)^{72}\right)}{\left(\left(1+0.00125\right)^{72}-1\right)}[/tex]

which is equal to 951.53

This number is our monthly payment

so for the full cost is [tex]951.53*12*6[/tex]

that equals 68510.16

now for when interest is equal to 6%

[tex]45000\cdot\frac{\left(0.0005\left(0.0005+1\right)^{72}\right)}{\left(\left(1+0.0005\right)^{72}-1\right)}[/tex]

this is equal to [tex]745.78*12*6[/tex]

so for the full cost is

so the extra interest is equal to the larger number minus the smaller one

[tex]68510.16-53696.16[/tex]

which equals

14,814.00 exactly

*mic drop

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