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The Ajax Co. just decided to save $1,500 a month for the next five years as a safety net for recessionary periods. The money will be set aside in a separate savings account which pays 3.25% interest compounded monthly. It deposits the first $1,500 today. If the company had wanted to deposit an equivalent lump sum today, how much would it have had to deposit?

Respuesta :

Answer:

Ans. Ajax Co. would have to pay an equivalent lump sum today of $81,689.29  

Explanation:

Hi, first we have to convert this 3.25% compounded monthly into an effective monthly rate, that is 0.0325/12 = 0.002708333 .

Since the first payment is made today, we assumed that this is an advance annuity, therefore, the equivalent lump sum to pay today is the present value of 59 monthly payments of $1,500, therefore we need to use the following formula.

[tex]PresentValue=\frac{A((1+r)^{n}-1) }{r(1+r)^{n} }[/tex]

Where:

A= $1,500

r = 0.002708333

n = 59

That is:

[tex]PresentValue=\frac{1,500((1+0.002708333)^{59}-1) }{0.002708333(1+0.002708333)^{59} } =\frac{1,500(0.173013023)}{0,00317691} = 81,689.29[/tex]

Best of luck.

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