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A company borrows $21,000 to purchase a new piece of equipment. The loan will be repaid in one lump sum at the end of 8 years. The bank offers to loan the money at 0.5% per month, but the company prefers to repay the loan at 6% per year. If the company is successful at getting the bank to agree to its preferred terms, how much will the company save in interest on the loan? Express your answer in $ to the nearest whole $.

Respuesta :

sebastiansierraocm

Answer:

$509

Explanation:

First, we find the lump sum to pay under the bank terms. The interest rate is 0.5% monthly, which is equivalent to 6.2% annually.

The formula is:

[tex]P (1 + i)^{n} = X[/tex]

Where:

  • P = Present value
  • i = interest rate
  • n = number of compounding periods of the interest rate
  • X = lump sum we need to find

Now, we simply plug the amounts into the formula:

[tex]$21,000 (1 + 0.062)^{8} = X\\[/tex]

[tex]33,979 = X[/tex]

Next, we find the value of the lump sum under the company's preferred terms:

[tex]21,000 (1 + 0.06)^{8} = X[/tex]

[tex]33,470 = X[/tex]

Finally, we susbtract the two figures to find the difference:

[tex]39,979 - 33,470[/tex] [tex]= 509[/tex]

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