Find the rate of simple interest per annum, if a sum borrowed becomes double in 5 years.

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To find the rate of simple interest per annum, we can use the formula for simple interest:

$$
A = P(1 + rt)
$$

Where:
- $$ A $$ is the total amount after time $$ t $$,
- $$ P $$ is the principal amount (the initial sum borrowed),
- $$ r $$ is the rate of interest per annum (in decimal),
- $$ t $$ is the time in years.

In this case, we know that the sum borrowed becomes double in 5 years. Therefore, we can express this as:

$$
A = 2P
$$

Substituting this into the simple interest formula gives us:

$$
2P = P(1 + r \cdot 5)
$$

Now, we can simplify this equation. First, divide both sides by $$ P $$ (assuming $$ P \neq 0 $$):

$$
2 = 1 + 5r
$$

Next, we can isolate $$ r $$:

$$
2 - 1 = 5r
$$
$$
1 = 5r
$$
$$
r = \frac{1}{5}
$$

Now, converting $$ r $$ into a percentage:

$$
r = \frac{1}{5} \times 100\%
$$
$$
r = 20\%
$$

Thus, the rate of simple interest per annum is $$ 20\% $$.
The rate of simple interest per annum is 20%.

Find the rate of simple interest per annum, if a sum borrowed becomes double in 5 years.

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