What is the initial amount if you earn interest of R320 in 9 months at a simple interest rate of 12% per year
We can solve for the initial amount using the simple interest formula:
Simple Interest = (Principal x Rate x Time) / 100
Where:
Simple Interest = R320
Rate = 12% per year
Time = 9/12 years (9 months is 3/4 of a year)
Substituting the given values:
R320 = (Principal x 12 x 3/4) / 100
Multiplying both sides by 100 and dividing by 12 x 3/4:
R320 x 4 x 100 / 12 x 3 = Principal
Simplifying the fraction:
R320 x 400 / 36 = Principal
R320 x 100 / 9 = Principal
Principal = R3,555.56 (rounded to the nearest cent)
Therefore, the initial amount is R3,555.56 if you earn interest of R320 in 9 months at a simple interest rate of 12% per year.
At what annual simple interstate rate should 96 be invested for 5 months, so as to produce the same interest earned if 75 was invested at 10% per annum for 1 year?
We can start by calculating the interest earned on the second investment of R75 at a simple interest rate of 10% per annum for 1 year.
Simple Interest = (Principal × Rate × Time) / 100
Simple Interest = (R75 × 10% × 1) / 100
Simple Interest = R7.50
Now we need to find the annual simple interest rate, r, for an investment of R96 for 5 months (which is equivalent to 5/12 of a year) that will produce the same interest earned of R7.50.
Simple Interest = (Principal × Rate × Time) / 100
R7.50 = (R96 × r × 5/12) / 100
R7.50 = R4r / 5
r = (5 × R7.50) / R4
r = 18.75%
Therefore, an annual simple interest rate of 18.75% is required for an investment of R96 for 5 months to produce the same interest earned as an investment of R75 at 10% per annum for 1 year.
To find the initial amount, or principal, we can use the formula for simple interest:
Simple Interest = Principal * Rate * Time
In this case, we are given the interest earned (R320), the interest rate per year (12%), and the time period (9 months).
First, let's convert the time period to years. Since there are 12 months in a year, 9 months is equivalent to 9/12 = 0.75 years.
Now we can rearrange the formula to solve for the principal:
Principal = Simple Interest / (Rate * Time)
Substituting the given values:
Principal = R320 / (0.12 * 0.75)
Next, we can calculate the value of the denominator:
Denominator = 0.12 * 0.75
Finally, we can find the initial amount:
Principal = R320 / Denominator
Calculating the value of the denominator:
Denominator = 0.12 * 0.75 = 0.09
Substituting the value of the denominator into the formula:
Principal = R320 / 0.09
Principal = R3555.56
Therefore, the initial amount is R3555.56.