randy had saved 5000 in an account that offered r% simple interest per annum on 20 march 2008. If the interest on 6 june 2008 was 40, find the exacttime of the investment
To find the exact time of the investment, we need to calculate the number of days between 20th March 2008 and 6th June 2008.
First, let's find the interest earned during this period. The formula for simple interest is:
Interest = (Principal * Rate * Time) / 100
We are given that the interest earned is 40 and the principal amount is 5000. Let's substitute these values into the formula:
40 = (5000 * R * Time) / 100 ....(1)
Now, we need to find the rate. We can rearrange equation (1) to solve for the rate (R):
R = (40 * 100) / (5000 * Time)
R = 0.8 / (Time) ....(2)
Next, we will calculate the number of days between 20th March 2008 and 6th June 2008.
20th March to 31st March = 11 days (remaining in March)
1st April to 30th April = 30 days
1st May to 31st May = 31 days
1st June to 6th June = 6 days
Now, adding up the days:
11 + 30 + 31 + 6 = 78 days.
To find the exact time, we will convert the interest rate to a fractional form by dividing it by 100:
R = 0.8 / 100
R = 0.008
Now, let's substitute the known values into equation (2):
0.008 = 0.8 / (Time)
Cross-multiplying:
0.008 * Time = 0.8
Now, we can solve for Time:
Time = 0.8 / 0.008
Time = 100
Therefore, the time of the investment is 100 days.
The exact time of the investment is 100 days between 20th March 2008 and 6th June 2008.