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.