Question 1

If you sign a discount note for $4,200 at a bank discount rate of 9%, for 90 days, what is the effective interest rate? (Round to the nearest tenth percent)

Accepted Answer

The effective interest rate is calculated by dividing the actual interest paid by the proceeds of the loan, then annualizing it. For a $4,200 note at a 9% discount rate for 90 days, the interest paid is $4,200 * 9% * (90/360) = $94.50. The proceeds of the loan are $4,200 - $94.50 = $4,105.50. The effective interest rate is ($94.50 / $4,105.50) * (360/90) = 9.2%.

Question 2

What are the proceeds of a note for $10,500 at a discount rate of 5%, for 30 months?

Accepted Answer

The proceeds of a note are calculated by subtracting the discount from the face value of the note. The discount is calculated as Discount Rate * Time in Years * Face Value. For a $10,500 note at a 5% discount rate for 30 months (or 2.5 years), the discount is 0.05 * 2.5 * $10,500 = $1,312.50. Therefore, the proceeds are $10,500 - $1,312.50 = $9,187.50.

Question 3

Velvety Smooth Linens takes out a loan of $3,500, for 314 days. If the amount of interest is $83.29, use the exact interest method to find the rate. (Round to nearest tenth percent)

Accepted Answer

The exact interest method uses a year of 365 days to calculate the interest rate. The formula for interest is $I = PRT$, where $I$ is the interest amount, $P$ is the principal amount, $R$ is the rate, and $T$ is the time in years. Rearranging the formula to solve for $R$, we get $R = \frac{I}{PT}$. Substituting the given values, $R = \frac{83.29}{3500 \times (314/365)}$, which calculates to approximately 0.028 or 2.8% when converted to a percentage.

Question 4

Toby signed a simple discount promissory note for $20,000. The discount rate is 8.5%, and the term of the note is 90 days. What are Todd's proceeds on the loan?

Accepted Answer

The proceeds of a simple discount note are calculated as the face value minus the discount. The discount is calculated as the face value multiplied by the discount rate multiplied by the term of the note. In this case, the proceeds are $20,000 - ($20,000 x 0.085 x 90/360) = $19,575.

Question 5

Caridad borrowed $15,500 at 11% ordinary interest for 120 days. After 70 days, she made a partial payment of $3,000. What is the final amount due on the loan? (Round to the nearest cent)

Accepted Answer

The interest for 70 days is calculated first, then the partial payment is subtracted. The remaining balance accrues interest for the remaining 50 days. The final amount due is calculated by adding this interest to the remaining balance.

Question 6

Use the ordinary interest method to find the rate of interest that Valley Mountain Vineyards pays on a loan of $5,500 for 234 days, if the amount of interest is $345.67. (Round to nearest tenth percent)

Accepted Answer

The ordinary interest method uses a 360-day year. The formula is Interest = Principal x Rate x Time. Solving for Rate: Rate = Interest / (Principal x Time). Substituting the given values: Rate = $345.67 / ($5,500 x 234/360) = 0.097, which is 9.7% when rounded to the nearest tenth percent.

Question 7

Alicia borrowed $8,500 at 6% ordinary interest for 180 days. After 40 days, she made a partial payment of $2,000. After another 70 days, Alicia made a second partial payment of $2,000. What is the final amount due on the loan? (Round to the nearest cent)

Accepted Answer

The final amount due on the loan, after calculating the ordinary interest on the initial amount and subsequent partial payments, and adjusting for the payments made, is $4,687.21.

Question 8

Shaylash takes out a loan for $10,500, at 8.5% exact interest. If the amount of interest is $858.03, what is the time period of the loan? (Round any fraction to the next higher day)

Accepted Answer

The answer of Shaylash takes out a loan for $10,500,...

Question 9

Suppose you take out a loan for $5,000, at 6% ordinary interest. If the amount of interest is $91.67, what is the time period? (Round to next higher day)

Accepted Answer

The formula for ordinary interest is I = PRT/360. Plugging in the values: 91.67 = 5000 * 0.06 * T / 360. Solving for T gives approximately 111 days.

Question 10

Suppose you take out a loan for $9,000, at 12% ordinary interest. If the amount of interest is $762.00, what is the time period? (Round any fraction to the next higher day)

Accepted Answer

The interest is calculated as:Interest = Principal * Rate * Time$762 = $9,000 * 0.12 * TimeTime = 762 / (9000 * 0.12) = 254 days

Question 11

What is the time period of a loan for $2,500, at 12% exact interest, if the amount of interest is $118.36? (Round to next higher day)

Accepted Answer

The time period of a loan can be calculated using the formula: Time = (Interest * 365) / (Principal * Rate)Plugging in the given values, we get: Time = (118.36 * 365) / (2500 * 0.12) = 145 days.Therefore, the correct answer is C) 145 days.

Question 12

Myerson borrowed $8,500 at 9% ordinary interest for 200 days. After 120 days, he made a partial payment of $4,000. What is the final amount due on the loan?

Accepted Answer

The answer of Myerson borrowed $8,500 at 9% ordinary interest...

Question 13

What is the time period of a loan for $3,000, at 10% ordinary interest, if the amount of interest is $145.00? (Round any fraction to the next higher day)

Accepted Answer

The answer of What is the time period of a...

Question 14

What is the rate of interest on a loan of $2,000, for 284 days, if the amount of interest is $93.37, using the exact interest method? (Round your answer to the nearest tenth percent)

Accepted Answer

The exact interest method takes into account the exact number of days in the year, which is 365 or 366 in a leap year. The formula for exact interest is:Interest = Principal x Rate x Time / 365$93.37 = $2,000 x Rate x 284 / 365Rate = 93.37 x 365 / 2,000 x 284Rate = 0.06004 or 6.0%

Question 15

Use the ordinary interest method to find the rate of interest that Make Over Picture Photo pays on a loan of $8,000 for 285 days, if the amount of interest is $590.00. (Round your answer to the nearest tenth percent)

Accepted Answer

The ordinary interest method (using a 360-day year) calculates interest as $I = PRT$, where $I$ is interest, $P$ is principal, $R$ is rate, and $T$ is time in years. Here, $I = $590$, $P = $8,000$, and $T = 285/360$ years. Solving for $R$, we get $R = I / (PT)$, which gives $R = 0.093$ or 9.3%.

Question 16

Use the exact interest method to find the rate of interest that Veldez Decks pays on a loan of $9,000 for 354 days, if the amount of interest is $489.50. (Round your answer to the nearest tenth percent)

Accepted Answer

The answer of Use the exact interest method to find...

Question 17

Find the amount of the principal on a loan at 6% interest for 274 days if the interest was $68.50, using the ordinary interest method. (Round to the nearest whole dollar amount)

Accepted Answer

The ordinary interest method uses a 360-day year. The formula for interest is I = PRT, where I is interest, P is principal, R is rate, and T is time in years. Rearranging gives P = I / (RT). Here, I = $68.50, R = 0.06, and T = 274/360. Solving gives P ≈ $1,500.

Question 18

Ada signed a simple discount promissory note for $5,500. The discount rate is 12%, and the term of the note is 5 months. What are Ada's proceeds on the loan?

Accepted Answer

The proceeds on the loan can be calculated by subtracting the discount from the face value of the note. The discount is calculated as: $ \text{Discount} = \text{Principal} \times \text{Rate} \times \text{Time} $, where the time is in years. For Ada's loan: $ \text{Discount} = \$5,500 \times 12\% \times \frac{5}{12} = \$275 $. Therefore, the proceeds are: $ \$5,500 - \$275 = \$5,225 $.

Question 19

Suppose you take out a loan for 180 days in the amount of $13,500 at 11% ordinary interest. After 50 days, you make a partial payment of $1,000. What is the final amount due on the loan? (Round to the nearest cent)

Accepted Answer

First, calculate the interest on the original loan for 180 days: Interest = Principal × Rate × Time = $13,500 × 11% × (180/360) = $742.50. After 50 days, a payment of $1,000 is made, reducing the principal to $12,500. The interest on the new principal for the remaining 130 days is: Interest = $12,500 × 11% × (130/360) = $401.04. The total amount due is the new principal plus the total interest: $12,500 + $742.50 + $401.04 = $13,643.54. However, since the payment reduces the principal before the total interest calculation, the correct approach is to first calculate the interest for 50 days on the original amount, then reduce the principal and calculate the remaining interest. Correcting this: Initial interest for 50 days = $13,500 × 11% × (50/360) = $206.25. New principal after payment = $13,500 - $1,000 = $12,500. Remaining interest for 130 days = $12,500 × 11% × (130/360) = $401.04. Total interest = $206.25 + $401.04 = $607.29. Final amount due = $12,500 + $607.29 = $13,107.29. The calculation provided does not match any of the options exactly due to a mistake in the interest calculation steps. The correct method involves calculating the interest before and after the payment, then summing those interests with the reduced principal. The error in calculation led to an incorrect conclusion. The correct calculation should consider the impact of the partial payment on both the reduction of principal and the adjustment of interest accrued before and after the payment. The final amount due involves calculating the interest up to the payment, reducing the principal by the payment amount, then calculating the interest on the new principal for the remainder of the term. The correct answer, based on the initial calculation method provided, was not accurately derived due to a miscalculation of the interest and the effect of the partial payment. To accurately determine the final amount due, one must correctly apply the formula for ordinary interest, adjust the principal after the partial payment, and calculate the interest on the adjusted principal for the remaining term.

Question 20

Suppose that you took out a loan at 12% interest for 200 days. If the amount of interest was $690.41, use the exact interest method to find the amount of principal you borrowed. (Round to the nearest whole dollar amount)

Accepted Answer

The exact interest method calculates interest using a 365-day year. The formula for interest is $I = P \times r \times \frac{t}{365}$, where $I$ is the interest, $P$ is the principal, $r$ is the annual interest rate, and $t$ is the time in days. Rearranging the formula to solve for $P$, we get $P = \frac{I}{r \times \frac{t}{365}}$. Plugging in the given values ($I = 690.41$, $r = 0.12$, $t = 200$), we find $P = \frac{690.41}{0.12 \times \frac{200}{365}}$, which calculates to approximately $10,500.00.

Quiz 10: Simple Interest and Promissory Notes