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A small foundry agrees to pay $420,000 three years from now to a supplier for a given amount of coking coal. The foundry plans to deposit a fixed amount in a bank account every three months, starting three months from now, so that at the end of three years the account holds $420,000. If the account pays 8.5% APR compounded monthly, how much must be deposited every three months?
a. $31,069.
b. $28,473.
c. $47,943.
d. $35,389.

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facundobuzzetti

Answer:

The correct answer is A.

Explanation:

Giving the following information:

Future Value= $420,000

Number of periods (n)= 4*3= 12 quarters

Interest rate (i)= 0.085/4= 0.0213

To calculate the quarterly deposit, we need to use the following formula:

FV= {A*[(1+i)^n-1]}/i

A= quarterly deposit

Isolating A:

A= (FV*i)/{[(1+i)^n]-1}

A= (420,000*0.0213) / [(1.0213^12) - 1]

A= $31,086.79

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