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A company needs $4,900,000 in 13 years in order to expand their factory. How much should the company invest each week if the investment earns a rate of 6.3% compounded weekly

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Final answer:

To achieve the future value of $4,900,000 in 13 years with a weekly compounded interest rate of 6.3%, the company must calculate the weekly payment using the future value of a series formula for compound interest.

Step-by-step explanation:

The question involves calculating how much a company should invest each week so that it can achieve a goal of $4,900,000 in 13 years, with an investment that has a 6.3% annual interest rate compounded weekly. To find this, we need to use the future value of a series formula for compound interest, which is:

FV = P × {[((1 + r/n)^(nt)) - 1] / (r/n)}

Where FV is the future value, P is the weekly payment, r is the annual interest rate (in decimal form), n is the number of times the interest is compounded per year, and t is the number of years.

First, convert the interest rate from a percentage to a decimal by dividing by 100: r = 6.3% = 0.063. Given that the interest is compounded weekly, n = 52. The time period is t = 13 years. The desired future value, FV, is $4,900,000.

Now, we can rearrange the formula to solve for P, the weekly payment:

P = FV / {[((1 + r/n)^(nt)) - 1] / (r/n)}

Next, we'll replace the variables with the actual numbers and calculate:

P = $4,900,000 / {[((1 + 0.063/52)^(52*13)) - 1] / (0.063/52)}

P = $4,900,000 / {[((1 + 0.0012115)^(676)) - 1] / 0.0012115} = $4,900,000 / {[1.020452976 - 1] / 0.0012115}

Completing the calculations will give the company the amount it needs to invest each week to reach its $4,900,000 goal.

User Ramon Diogo
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