At what rate of annual simple interest, a certain sum will amount to four times in 15yr
use a random number to use for the sum Ex. 300 is going to be the sum we are using and then Im going to use i for the interest rate so it doesn't get confusing with the variables
300=sum
i=interest rate
300xi^15=300x4
300xi^15=1200
i^15= 4
15square root of 4 = 1.09682498
first, simple interest, not compound
second, no random amount needs to be devised. We just want
(1+15r) = 4
r = 0.2 = 20%
sounds right, since at 20%, the original amount is added every 5 years. So, after 15 years, that has happened 3 times, making the balance 4 times the original amount.
To find the rate of annual simple interest, we need to use the formula:
Simple Interest = (Principal * Rate * Time) / 100
Let's break down the given information:
Principal: The initial sum of money.
Amount: The final amount after 15 years.
Time: The number of years.
In this case, the amount is four times the principal. So, we can write it as:
Amount = 4 * Principal
Using the formula for simple interest, we can also write it as:
Amount = Principal + Simple Interest
Substituting the values, we get:
4 * Principal = Principal + Simple Interest
Simplifying it further, we have:
3 * Principal = Simple Interest
Now, we can rewrite the simple interest formula as:
Simple Interest = (3 * Principal * Rate * Time) / 100
Given that the time is 15 years, the equation becomes:
Simple Interest = (3 * Principal * Rate * 15) / 100
Since we want to find the rate of interest, we can rearrange the equation as:
Rate = (Simple Interest * 100) / (3 * Principal * Time)
Therefore, to determine the rate of annual simple interest, we need the values of the simple interest, principal, and time.