Final answer:
Calculating the simple interest for a $6500 investment at a 6.4% annual rate over 120 days, we find that the investment will grow to $6725.21 after 120 days.
Step-by-step explanation:
To calculate the simple interest on a $6500 investment at a 6.4% annual interest rate over 120 days, we use the formula for simple interest, which is I = P x r x t.
In this context, I is the interest, P is the principal amount ($6500), r is the annual interest rate (6.4% or 0.064 as a decimal), and t is the time the money is invested for, in years.
Since we are calculating for 120 days, we must convert this period to years because the interest rate is annual.
There are 365 days in a year, so 120 days is equivalent to 120/365 years. We can now calculate the interest:
I = $6500 × 0.064 × (120/365)
= $225.21
Now to find the total amount of the investment after 120 days, we add the interest to the principal amount:
Total = Principal + Interest
Total = $6500 + $225.21
= $6725.21
Thus, the investment will be worth $6725.21 after 120 days.