A sum of money triples itself in 10 years at a certain rate of compound interest. What is the rate of interest?

To find the rate of interest, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where: A = the final amount P = the principal amount (initial sum of money) r = the annual interest rate (in decimal form) n = the number of times interest is compounded per year t = the number of years

In this case, we know that the sum of money triples itself in 10 years. This means that the final amount (A) is three times the principal amount (P).

So, we can rewrite the formula as:

3P = P(1 + r/n)^(nt)

Now, we can simplify the equation:

3 = (1 + r/n)^(nt)

Since we are given that the money triples itself in 10 years, we can substitute t = 10 into the equation:

3 = (1 + r/n)^(10n)

To solve for the rate of interest (r), we need to find the value of r/n. We can do this by trial and error or by using a calculator or spreadsheet program.

Let's assume that n = 1 (compounded annually) for simplicity. We can then rewrite the equation as:

3 = (1 + r/1)^(10*1) 3 = (1 + r)^10

Now, we can solve for (1 + r) by taking the 10th root of both sides:

(1 + r) = 3^(1/10)

Finally, we can solve for r by subtracting 1 from both sides:

r = 3^(1/10) - 1

Using a calculator, we can find that:

r ≈ 0.259

Therefore, the rate of interest is approximately 25.9%.