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Travis International has a debt payment of $2.34 million that it must make 6 years from today. The company does not want to come up with the entire amount at that time, so it plans to make equal monthly deposits into an account starting 1 month from now to fund this liability. If the company can earn a return of 5.33 percent compounded monthly, how much must it deposit each month

Respuesta :

Answer:

$27,692.31

Explanation:

Principle amount = $2.34 million = $2,340,000

Time, n = 6 years = 72 months

Rate of interest = 5.33%

Monthly rate of interest, r = 5.33% ÷ 12 = 0.44% = 0.0044

Compounded monthly

FV of Annuity = ( Monthly deposits ) × { [ ( 1 + r )ⁿ - 1 ] ÷ r }

or

$ 2,340,000 = ( Monthly deposits ) × { [ ( 1 + 0.0044 )⁷² - 1 ] ÷ 0.0044 }

or

$2,340,000 = ( Monthly deposits ) × { [  1.3718 - 1  ] ÷ 0.0044 }

or

$2,340,000 = ( Monthly deposits ) × [ 0.3718 ÷ 0.0044 ]

or

$2,340,000 = ( Monthly deposits ) × 84.5

or

Monthly deposits = $27,692.31

Answer:

P = $27,692.307

Explanation:

GIven data:

debt payment is $2.34 million

duration of debt 6 year

future value is 2.34 million

rate is 5.33% per annum = 0.44% per month

annuity formula is given as

[tex]FV = \frac{P \times [(1+ r)^{n} -1 ]}{r}[/tex]

[tex]2340000 = \frac{P \times(1+0.0044)^{72} -1]}{0.0044}[/tex]

[tex]\frac{2340000 \times 0.0044}{0.3718} = P[/tex]

P = $27,692.307

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