on what day will 8,000 earn 180 interest when invested on April 25, 2002 at 9% simple interest? use ordinary interest and actual time.
date of investment sept. 4, 2002 and date of maturity feb. 12, 2003. what is the approximate no. days and actual no. of days?
I = PRT
8000(.09)T = 180
T = .25 years or 91 days
I will leave it up to you to calculate what date that is
To determine the day when an investment of $8,000 will earn $180 at a simple interest rate of 9% using the ordinary interest method and actual time, we need to calculate the time it would take for the investment to accumulate the desired interest.
The formula to calculate simple interest is:
I = P * r * t
Where:
I = Interest
P = Principal (initial investment)
r = Interest rate per time period
t = Time (in years)
In this case, we have:
P = $8,000
I = $180
r = 9% (or 0.09 in decimal form)
t = ?
Rearranging the formula, we can solve for t:
t = I / (P * r)
t = 180 / (8,000 * 0.09)
t ≈ 0.025 (approximately)
Now, we need to convert this decimal value into a time period. Since the interest is calculated from April 25, 2002, we can convert the decimal value of time (0.025) into days.
To convert decimal years into days, we use the following conversion:
1 year = 365 days
t (in days) = t (in years) * 365
t (in days) ≈ 0.025 * 365
t (in days) ≈ 9.125
So, it would take approximately 9.125 days for an investment of $8,000 at 9% simple interest to accumulate $180.
Therefore, the investment will earn $180 in interest by May 4, 2002, which is the 9th day after April 25, 2002.
To determine the day when 8,000 will earn 180 in interest at a simple interest rate of 9%, we need to calculate the time it will take for the interest to accumulate to that amount.
First, let's convert the interest rate from a yearly rate to a daily rate, as we are dealing with the "actual time" using simple interest.
The daily interest rate can be calculated by dividing the yearly rate by 365 (days in a year):
Daily interest rate = (9% / 100) / 365 = 0.0002465753
Next, we need to determine the number of days it will take for the account to accumulate 180 in interest.
Interest = Principal x Rate x Time
180 = 8,000 x 0.0002465753 x Time
Now, we can solve for Time:
Time = 180 / (8,000 x 0.0002465753)
Time ≈ 0.09183673469 years
To find the number of days, we multiply the fractional part by 365:
Time in days = 0.09183673469 x 365
Time in days ≈ 33.5 days
Since we are starting on April 25, 2002, we need to count forward 33.5 days from that date to find the approximate day when the interest will accumulate. However, please note that there can be some variation in the exact day due to factors like leap years.
Approximate day = April 25, 2002 + 33.5 days
Using this calculation, we estimate that the interest of 180 will accumulate around May 28 or May 29, 2002.