lley Company made plans to construct a new factory at an estimated cost of he co

Question

lley Company made plans to construct a new factory at an estimated cost of he construction will begin on 1/1/x6. The company decided to prepare for this expenditure, as follows a) On January 1, 20x1, $2,000,000 was deposited into a "construction fund"; the fund will earn interest at an annual rate of 6%, compounded semi-annually. b) The company started to make semi-annual contributions into the "construction fund" to help bring the needed amount (at 1/1/x6) to $10,000,000. Payments into the fund will occur on January 1st and July 1st - with the first payment occurring on July 1, 20x1 and the last payment occurring on July 1, 20x5. (As stated earlier, the fund will earn interest at an annual rate of 6%, compounded se annually.) REQUIRED: Determine the amount of each of the semi-annual contributions into th "construction fund" so that the company reaches its $10,000,000 goal on January 1, 20x6. (8 points) Amount of each semi-annual contribution: $

Explanation / Answer

Interest for six month = 6 / 2 = 3%

Let semi annual contribution be = y

Hence as per the equation,

$10,000,000 = [y x (1.03)9] + [y x (1.03)8] + [y x (1.03)7] + [y x (1.03)6] + [y x (1.03)5] + [y x (1.03)4] + [y x (1.03)3] + [y x (1.03)2] + [y x (1.03)1]

$10,000,000 = (y x 1.3048) + (y x 1.2668) + (y x 1.2299) + (y x 1.1941) + (y x 1.1593) + (y x 1.1255) + (y x 1.0927) + (y x 1.0609) + (y x 1.03)

$10,000,000 = 10.464y

y = $955,657

Hence amount of each semi annual contribution = $955,657

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