To find out how much the company should invest each week, we can use the future value formula for compound interest:
FV = PV × (1 + r/n)^(nt)
Where:
- FV is the future value (the amount needed in 10 years, $4,000,000).
- PV is the present value (the initial investment).
- r is the annual interest rate (7%, or 0.07).
- n is the number of times the interest is compounded per year (weekly compounding means n = 52).
- t is the time the money is invested for in years (10 years).
We need to solve for PV, the present value (initial investment).
Let's calculate it.
To calculate the weekly investment amount, we rearrange the formula to solve for PV:
PV = FV / (1 + r/n)^(nt)
Substituting the given values:
PV = $4,000,000 / (1 + 0.07/52)^(52*10)
Now, let's compute the present value.
After calculating, the present value (initial investment) required is approximately $1,926,227.41.
So, the company should invest about $1,926,227.41 each week in order to have $4,000,000 in 10 years with a 7% interest rate compounded weekly.
