Margaret received $671.50 in cash as proceeds from a loan of $680.00 The discount rate was 10% simple interest. Find the discount period in months.
Hummm. With simple interest, a rate of 10% on $680, in one month the balance would be 680*(1+(0.1/12)) = 685.66666. Ergo, the monthly payment would be 5.66666. So then number of months to make 671.5 would be (671.5/5.66666) = 118.5
To find the discount period in months, we need to determine the number of months it will take for Margaret to repay the loan by making monthly payments.
To do this, we can use the formula for simple interest:
Interest = Principal * Rate * Time
Since we need to find the time (number of months), we rearrange the formula as:
Time = Interest / (Principal * Rate)
Let's plug in the given values:
Principal = $680.00
Rate = 10% (0.10)
Interest = $680.00 - $671.50 = $8.50
Now, we calculate the time:
Time = $8.50 / ($680.00 * 0.10)
Time = $8.50 / $68.00
Time ≈ 0.125
Since Time is measured in years, we need to convert it to months. There are 12 months in a year, so:
Time in months = 0.125 * 12
Time in months ≈ 1.5 months
Therefore, the discount period is approximately 1.5 months.
To find the discount period in months, we need to calculate the number of months it takes to repay the loan with the monthly payment of $5.66666 and reach a total payment of $671.50.
So, the number of months would be (671.50 / 5.66666) = 118.5 months.
Since the discount period is generally counted in whole months, we can round the answer to the nearest whole number. Therefore, the discount period is approximately 119 months.