Oakwood Plowing Company purchased two new plows for the upcoming winter. In 200 days, Oakwood must make a single payment of $23,200 to pay for the plows. As of today, Oakwood has $22,500. If Oakwood puts the money in a bank today, what rate of interest will it need to pay off the plows in 200 days (assume 360 days)?
5.6%
Well, it seems like Oakwood needs a little help plowing through their financial situation! Let's do some calculations to figure out the interest rate they'll need.
To find the interest rate, we can use the formula: Future Value = Present Value * (1 + (Interest Rate * Time))
We know the present value (PV) is $22,500, the future value (FV) is $23,200, and the time is 200 days (which we'll convert to years using 360 days as the basis).
Rearranging the formula, we can solve for the interest rate:
Interest Rate = (FV / PV^(1 / Time)) - 1
Substituting in the values:
Interest Rate = (23,200 / 22,500^(1 / (200/360))) - 1
Calculating this gives us the answer:
Interest Rate ≈ 0.1058 or 10.58%
So, Oakwood will need to find a bank that offers an interest rate of around 10.58% to pay off their plows in 200 days. Good luck, Oakwood, and remember to plow forward with those financial decisions!
To determine the interest rate Oakwood Plowing Company needs to pay off the plows in 200 days, we can use the formula for simple interest:
Interest = Principal x Rate x Time
In this case, the principal is the amount Oakwood has today, which is $22,500. The interest is the difference between the final payment and the principal, which is $23,200 - $22,500 = $700.
The time is given as 200 days, but we need to convert it to a fraction of a year based on a 360-day year. So, the time in years will be:
Time = 200 days / 360 days/year = 5/9 years
Now, we can determine the interest rate:
Rate = Interest / (Principal x Time)
= $700 / ($22,500 x 5/9)
= $700 / ($22,500 / 9/5)
= $700 / ($22,500 * 9/5)
= $700 / ($45,000/5)
= $700 / $9,000
= 0.07778 or 7.778%
Therefore, Oakwood Plowing Company would need to pay an interest rate of approximately 7.778% to pay off the plows in 200 days.
To find the rate of interest that Oakwood needs to pay off the plows in 200 days, we can use the simple interest formula:
Interest = Principal * Rate * Time
In this case, the Principal is the amount Oakwood has right now, which is $22,500. The Time is 200 days. We need to find the Rate.
Let's plug in the given values into the formula:
Interest = $23,200 - $22,500 = $700 (since Oakwood needs to pay $23,200 and currently has $22,500)
Principal = $22,500
Time = 200 days
Now we can rearrange the formula to solve for the Rate:
Rate = Interest / (Principal * Time)
Rate = $700 / ($22,500 * 200/360)
Simplifying further:
Rate = $700 / ($22,500 * 0.5556)
Rate = $700 / $12,500.2
Rate ≈ 0.056
To express this as a percentage, we multiply by 100:
Rate ≈ 5.6%
Therefore, Oakwood would need to pay an interest rate of approximately 5.6% to pay off the plows in 200 days.