Stephanie Venze signed a simple discount note for $3400 for 120 days at a rate of 12%. Find (a) the proceeds and (b) the effective interest rate based on the proceeds received by Venze.
Brenna earned 120 in simple interest in 9 months at an annual interest rate of 8%. How much money did she invest
To find the proceeds and the effective interest rate, we can use the formula for simple discount note:
Proceeds = Principal - Discount
Effective Interest Rate = (Discount / Principal) * (360 / t)
Given information:
Principal (P) = $3400
Rate (r) = 12%
Time (t) = 120 days
Step 1: Calculate the discount (D):
D = P * r * t
D = $3400 * 0.12 * (120/360)
D = $408
(a) The proceeds (P) can be found by subtracting the discount (D) from the Principal (P):
Proceeds = Principal - Discount
Proceeds = $3400 - $408
Proceeds = $2992
Therefore, the proceeds are $2992.
(b) To find the effective interest rate (EIR), we will use the formula:
Effective Interest Rate = (Discount / Principal) * (360 / t)
EIR = (D / P) * (360 / t)
EIR = ($408 / $3400) * (360 / 120)
EIR ≈ 0.12 * 3
EIR ≈ 0.36
Therefore, the effective interest rate based on the proceeds received by Venze is approximately 0.36 (or 36%).
To find the proceeds received by Stephanie Venze, we need to calculate the discount and subtract it from the face value of the note.
(a) Calculating the discount:
Discount = Face Value x Rate x Time
Here, the face value is $3400, the rate is 12% (or 0.12 in decimal form), and the time is 120 days (or 120/365 years, considering a non-leap year).
Discount = $3400 x 0.12 x (120/365) = $132.60
Proceeds = Face Value - Discount
Proceeds = $3400 - $132.60 = $3267.40
Therefore, the proceeds received by Stephanie Venze are $3267.40.
(b) To find the effective interest rate based on the proceeds received by Venze, we can use the following formula:
Effective Interest Rate = (Discount / Proceeds) x (365 / Time)
Plugging in the values:
Effective Interest Rate = ($132.60 / $3267.40) x (365 / 120) = (0.0406) x (3.042)
Effective Interest Rate ≈ 0.1236
Converting to a percentage, the effective interest rate is approximately 12.36%.
Therefore, the effective interest rate based on the proceeds received by Venze is approximately 12.36%.