RM 2000 was invested on 15march 2012. If the simple interest rate offered was 10% per annum, find the interest received on 29 August 2012 using
A. Exact time and exact simple interest
B. Exact time and ordinary simple interest
C. Approximate time and exact simple interest
D. Approximate time and ordinary simple interes
Exact simple interest means we count the number of days in the year (some say it is 365, leap year or not) to do the calculation of simple interest.
Ordinary simple interest is based on the banker's year of 12 months of 30 days, or 360 days a year. This is equivalent to a slightly higher interest rate.
Exact time means we calculate the loan duration by the number of days between the loan and repayment.
If we borrowed on January 1st 2012 to March 1st 2012, the exact time is 31+29 =60 days.
Approximate time is counting the number of complete months plus a certain number of days, if applicable. The extra days are divided by 30 to get a fraction of months.
Example:
Exact time and exact simple interest:
RM 2000 at 10% pa
March 15 to August 29.
Number of days:
16+30+31+30+31+29=167 days
Period: 167/366 year
Rate: 10%
Interest: RM 2000*(10/100)*167/366= RM 91.26 (to the nearest cent, 0.01RM)
To calculate the interest received on 29 August 2012, we first need to calculate the time period between 15 March 2012 and 29 August 2012. Then, we can use this time period to calculate the interest using the different methods mentioned.
A. Exact time and exact simple interest:
In this case, we will calculate the time period exactly in terms of years and use the formula for simple interest.
1. Calculate the time period:
The time between 15 March 2012 and 29 August 2012 is 5 months and 14 days. Since we need to calculate in terms of years, we convert this time period to years.
1 month = 1/12 year (approximately)
14 days = 14/365 year (approximately)
So, the exact time period in years is:
5 months + 14/365 year = 5/12 + 14/365 year
2. Calculate the interest:
Simple interest is calculated using the formula:
Interest = Principal x Rate x Time
Principal = RM 2000
Rate = 10% per annum = 0.1
Interest = 2000 x 0.1 x (5/12 + 14/365)
B. Exact time and ordinary simple interest:
In this case, we will calculate the time period exactly in terms of years and use the formula for ordinary simple interest.
The formula for ordinary simple interest is:
Interest = Principal x Rate x Time
The calculation is similar to the previous case, but we will use ordinary simple interest instead.
C. Approximate time and exact simple interest:
In this case, we will approximate the time period to get a rough estimate of the interest using exact simple interest.
1. Calculate the approximate time period:
We can round the time period to the nearest whole number of years.
The time between 15 March 2012 and 29 August 2012 is approximately 1 year.
2. Calculate the interest:
We can use the formula for simple interest using the approximate time period and exact simple interest.
Interest = Principal x Rate x Time
Interest = 2000 x 0.1 x 1
D. Approximate time and ordinary simple interest:
In this case, we will approximate the time period and use the formula for ordinary simple interest.
1. Calculate the approximate time period:
We can round the time period to the nearest whole number of years, just like in the previous case.
The time between 15 March 2012 and 29 August 2012 is approximately 1 year.
2. Calculate the interest:
We will use the formula for ordinary simple interest with the approximate time period.
Interest = Principal x Rate x Time
Interest = 2000 x 0.1 x 1
Now, you can solve the calculations for each method to find the interest received on 29 August 2012.