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Question 1177372: A company loaned 300 of its machines to a subsidiary company. If the subsidiary company was able to generate 7% compounded each quarter on its invested money, what total amount does it need to invest to purchase these machines within 18 months at a price of $300,000 each?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the total cost of the machines is 300 * 300,000 = 3 * 10^2 * 3 * 10^5 = 9 * 10^7 = 90,000,000 dollars.
the subsidiary company is able to generate 7% per year compounded quarterly on its invested money.
it needs to have 90 million dollars within 18 months.
1 quarter is equal to 3 months.
18 months / 3 = 6 quarters.
the formula to use is f = p * (1 + r) ^ n
f is the future value
p is the present value
r is the interest rate per time period
n is the number of time periods.
since the time periods are in quarters, you need to:
divide 7% per year by 4 to get (7/4)% per quarter.
since the formula works on rate rather than percent, you need to divide that by 100 to get a rate of 7/400 per quarter.
the number of quarters is 18 / 3 = 6 quarters.
that's because 1 quarter is equal to 3 months.
the future value is 90 million.
that's how much is needed in 18 months to buy the machines.
the formula becomes:
90 million = p * (1 + 7/400) ^ 6
divide both sides of this equation by (1 + 7/400) ^ 6 to get:
90 million / (1 + 7/400) ^ 6 = p
solve for p to get:
p = 81.10281875 million.
confirm by replacing p in the original equation with that and solve for f to get:
f = 81.10282875 * (1 + 7/400) ^ 6 = 90 million.
your solution is that the subsidiary company needs to invest 81.10282875 million now so that it can have 90 million available to purchase the machines in 18 months.
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