William owes $9,000.00 to a friend who is charging him interest of 1.60% p.m. he is required to settle the amount with 2 equal payments, one today and the other in 2 months. Calculate the size of the payments using 2 months as the focal date. Round your answer to 2 decimal places.
Well, it seems like William is in quite a pickle. Let's see if we can put a smile on his face while doing the math!
The first step is to calculate the interest for two months. Since the interest is charged at a rate of 1.60% per month, for two months, it would be 3.20% (2 times 1.60%). Keep that number handy, we'll need it later.
Now, let's calculate the total amount William needs to repay after two months. This will be the original debt of $9,000 plus the interest. To do this, we simply add the interest to the original debt:
$9,000 + ($9,000 * 3.20%) = $9,000 + $288 = $9,288.
So, after two months, William needs to repay $9,288.
Since William is required to settle the amount with 2 equal payments, we just divide that total by 2:
$9,288 / 2 = $4,644.
Therefore, the size of each payment William needs to make using 2 months as the focal date is $4,644.
I hope I was able to calculate that with enough humor to make you smile!
To calculate the size of the payments, we need to consider the principal amount, interest rate, and the duration.
Given:
Principal amount (P) = $9,000.00
Interest rate (r) = 1.60% per month
Duration (t) = 2 months
First, let's calculate the interest for the 2-month duration:
Interest (I) = P * r * t
Plugging in the values:
I = $9,000.00 * 0.016 * 2
I = $288.00
Next, let's determine the total amount to be paid:
Total amount = Principal amount + Interest
Total amount = $9,000.00 + $288.00
Total amount = $9,288.00
Since there are two equal payments, we divide the total amount by 2:
Payment size = Total amount / 2
Payment size = $9,288.00 / 2
Payment size = $4,644.00
Therefore, the size of each payment, rounded to 2 decimal places, is $4,644.00.
To calculate the size of the payments, we need to consider the loan amount, the interest rate, and the number of payments.
First, let's consider the loan amount. William owes $9,000.00.
Next, let's calculate the interest. The friend is charging him an interest rate of 1.60% per month. To calculate the interest for two months, we can use the formula: Interest = Loan Amount * Interest Rate * Number of Months.
For the first payment, which is due today, the interest is calculated for 2 months. So, the interest for the first payment is: Interest1 = $9,000.00 * 1.60% * 2.
For the second payment, which is due in 2 months, the interest is calculated for 1 month. So, the interest for the second payment is: Interest2 = $9,000.00 * 1.60% * 1.
Now, let's calculate the size of the payments. The total amount to be settled is the loan amount plus the interest for both payments. The total amount is: Total Amount = Loan Amount + Interest1 + Interest2.
Next, we divide the total amount by the number of payments to get the size of each payment. Since there are 2 equal payments, the size of each payment is: Payment Size = Total Amount / 2.
Now, let's plug in the values and calculate:
Interest1 = $9,000.00 * 1.60% * 2 = $<<9000*0.016*2=288.00>>288.00
Interest2 = $9,000.00 * 1.60% * 1 = $<<9000*0.016*1=144.00>>144.00
Total Amount = $9,000.00 + $288.00 + $144.00 = $<<9000+288+144=9428.00>>9428.00
Payment Size = $9,428.00 / 2 = $<<9428/2=4714.00>>4714.00
Therefore, the size of each payment, rounded to 2 decimal places, is $4714.00.