A person invests a certain sum at simple interest, and after one year, the amount becomes 13 times the principal. If the rate of interest per annum is numerically three times the time period in years, what is the rate of interest?

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**Solution:**

1. Let the principal amount be $P$, the rate of interest be $R\%$ per annum, and the time period be $T$ years.

2. According to the problem, the amount after one year is 13 times the principal, so:
   $$	ext{Amount} = 13P$$

3. The simple interest formula is:
   $$	ext{Simple Interest} = \frac{P 	imes R 	imes T}{100}$$

4. The interest earned is the amount minus the principal:
   $$13P - P = 12P$$

5. Equate the interest to the formula:
   $$12P = \frac{P 	imes R 	imes T}{100}$$

6. Simplify by dividing both sides by $P$:
   $$12 = \frac{R 	imes T}{100} \implies R 	imes T = 1200$$

7. Given that the rate of interest is three times the time period:
   $$R = 3T$$

8. Substitute $R$ in the equation:
   $$3T 	imes T = 1200 \implies 3T^2 = 1200 \implies T^2 = 400 \implies T = 20$$

9. Calculate $R$:
   $$R = 3 	imes 20 = 60$$

**Answer:** $60\%$

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