A certain sum of money doubles itself at simple interest in 8 years. In how many years will it be three times at the same rate

To determine how many years it will take for a certain sum of money to triple at the same rate of simple interest, we can break it down step by step. We know that the money doubles in 8 years. From this, we can first find the rate of interest, and then use that rate to calculate when the money will triple.

Finding the Rate of Simple Interest

In simple interest, the formula to calculate the total amount (A) after a certain time (t) is:

A = P + (P * r * t), where:

• P = principal amount (initial sum of money)
• r = rate of interest (as a decimal)
• t = time in years

Since the sum of money doubles in 8 years, we can express this situation mathematically. When the amount doubles, A = 2P. Plugging this into the formula gives us:

2P = P + (P * r * 8)

Simplifying the Equation

We can simplify this equation:

• 2P - P = P * r * 8
• P = P * r * 8

Assuming P is not zero, we can divide both sides by P:

1 = r * 8

This means:

r = 1/8 or 0.125 (which is 12.5% per annum)

Calculating the Time to Triple the Amount

Now that we know the rate of interest, we can find out how long it will take for the amount to become three times the principal. We want to find t when A = 3P:

3P = P + (P * r * t)

Again, simplifying this gives:

• 3P - P = P * r * t
• 2P = P * r * t

Dividing both sides by P:

2 = r * t

Substituting the value of r we found (0.125):

2 = 0.125 * t

Solving for t

To isolate t, we divide both sides by 0.125:

t = 2 / 0.125

Calculating this gives:

t = 16 years

Final Thoughts

Therefore, it will take 16 years for the original sum of money to triple at the same rate of simple interest. This method can be applied to any similar problems involving simple interest, making it a valuable skill to have!