Sorry i could not understand log. Could you explain it in simpler terms? I am in class 7.
The question was
if a sum of money doubles in 8 yrs, in how many years will it triple itself?Is the answer 16? If it is please tell me how to show the workings. I understood the concept but cannot express it.This is a simple interest sum.
If the money doubles in 8 years than in 16 years it would quadruple itself. So try between 8 and 16 years.
is it 12?
No, it is slightly less than 12.
No problem! I can explain it in simpler terms. The concept you are referring to is compound interest, not simple interest. Compound interest means that not only the original sum of money is earned interest, but also the accumulated interest over time earns additional interest.
Let's break down the problem into steps to solve it:
Step 1: Understand the given information:
- The initial sum of money doubles in 8 years. This means that if you start with $1, after 8 years, you would have $2.
- We need to find out in how many years the initial sum of money will triple itself.
Step 2: Define the variables:
- Let's say the initial sum of money is P.
- We need to find the time it takes for P to triple itself, so let's call it T.
Step 3: Write down the formula:
The compound interest formula is:
A = P(1 + r/n)^(nt)
Where:
- A is the final amount (in this case, tripling itself means A = 3P)
- P is the principal amount (the initial sum of money)
- r is the rate of interest (unknown in this case)
- n is the number of times that interest is compounded per year (since it's not mentioned, we assume it's compounded annually)
- t is the number of years (unknown in this case)
Step 4: Determine the values:
We know that A = 3P and n = 1 (compounded annually). So we can modify the formula to find the value of T:
3P = P(1 + r/1)^(1*T)
Dividing both sides by P:
3 = (1 + r)^T
Step 5: Solve the equation:
To solve for T, we can take the logarithm of both sides. In this case, we'll use the natural logarithm (ln):
ln(3) = T * ln(1 + r)
Step 6: Substitute the values:
ln(3) = T * ln(1 + r)
ln(3) = T * ln(1 + 0.1) [assuming an interest rate of 10% (0.1)]
Step 7: Solve for T:
To find the value of T, we divide both sides by ln(1 + 0.1):
T = ln(3) / ln(1 + 0.1)
Step 8: Calculate:
Using a calculator, you can find the value of T to be approximately 10.5.
So, the correct answer is not 16, but approximately 10.5 years. I hope that clarifies the solution for you!