Simple Interest Doubling and Tripling

Simple Interest Doubling and Tripling problems ask how long a principal takes to become two or three times its original value. Since simple interest is calculated only on the principal, the doubling time is 100 divided by the annual rate, while the tripling time is 200 divided by the annual rate.

On this page

What Are Simple Interest Doubling and Tripling Problems?

Under simple interest, doubling means the final amount becomes 2P, and tripling means it becomes 3P, where P is the principal. The required time depends only on the rate when the interest is calculated on the original principal.

For simple interest, A = P + SI and SI = PRT/100, where R is the rate percent per annum and T is time in years. For doubling, A = 2P, so SI = P. For tripling, A = 3P, so SI = 2P. Therefore, the time required is 100/R years for doubling and 200/R years for tripling.

Simple Interest Doubling and Tripling Formula & Tricks

Important Formulas

Simple Interest
SI = (P × R × T) / 100

P is the principal, R is the rate percent per period, and T is the time in the same period.

Amount
A = P + SI

The amount is the principal plus the simple interest earned.

SI Doubling Time
T = 100 / R

When the amount doubles, SI = P. Thus, PRT/100 = P, giving T = 100/R years when R is an annual rate.

SI Tripling Time
T = 200 / R

When the amount triples, SI = 2P. Thus, PRT/100 = 2P, giving T = 200/R years when R is an annual rate.

General Multiplication
For A = kP, T = 100(k - 1) / R

An amount k times the principal requires interest of (k - 1)P under simple interest.

Quick Tricks

Tripling Takes Twice the Doubling Time

Doubling needs interest equal to P, whereas tripling needs interest equal to 2P. At the same simple interest rate, tripling therefore takes twice as long.

Example: At 10% per annum, doubling time = 100/10 = 10 years and tripling time = 200/10 = 20 years.
Principal Does Not Affect the Time

In the equations for doubling and tripling, P cancels out. Therefore, for a fixed rate, the required time is the same for every principal.

Example: At 8% per annum, both Rs 5,000 and Rs 12,000 double in 100/8 = 12.5 years.

Simple Interest Doubling and Tripling Concepts

Amount Growth Under Simple Interest

Under simple interest, the interest added in every equal time period remains constant because it is calculated on the original principal.

The amount after T years is A = P(1 + RT/100). Unlike compound interest, previously earned interest is not added to the principal for later calculations. If the rate is R% per annum, the interest earned in one year is PR/100.

Example: For P = Rs 4,000, R = 5% per annum, and T = 3 years, SI = 4,000 × 5 × 3/100 = Rs 600, so A = Rs 4,600.

Doubling Time in Simple Interest

The amount doubles when the simple interest becomes equal to the principal.

Set A = 2P. Since A = P + SI, SI = P. Using PRT/100 = P and cancelling P gives RT = 100, so T = 100/R. The result is in years when R is an annual percentage rate.

Example: At 12.5% per annum, doubling time = 100/12.5 = 8 years.

Tripling Time in Simple Interest

The amount triples when the simple interest becomes twice the principal.

Set A = 3P. Then SI = 3P - P = 2P. Substituting in PRT/100 = 2P and cancelling P gives RT = 200, so T = 200/R.

Example: At 8% per annum, tripling time = 200/8 = 25 years.

Finding the Rate from Doubling or Tripling Time

The rate can be found by rearranging the time formulas: R = 100/T for doubling and R = 200/T for tripling.

For a principal to double in T years, R = 100/T percent per annum. For it to triple in T years, R = 200/T percent per annum. The time and rate must use matching units.

Example: If a sum triples in 16 years under simple interest, R = 200/16 = 12.5% per annum.

General Amount Multiplier

If the final amount is k times the principal, the required simple-interest time is T = 100(k - 1)/R.

Since A = kP and A = P + SI, the required interest is SI = (k - 1)P. Substitution into SI = PRT/100 gives the general formula. Doubling uses k = 2, and tripling uses k = 3.

Example: For an amount four times the principal at 10% per annum, T = 100(4 - 1)/10 = 30 years.

Simple Interest Doubling and Tripling Video Lessons

Watch short topic-wise lessons for quick revision.

6 Lessons
Lesson 1 of 6 Quick Revision

Simple Interest: Doubling, Tripling and N Times

Learn how to calculate the time required for a principal or amount to double, triple, or become N times under simple interest.

Continue with more lessons and practice in PrepShots.Watch More in App - Start ₹1 Trial →
More Simple Interest Doubling and Tripling Lessons Scroll to explore →

Practice Simple Interest Doubling and Tripling Questions

Practise published questions related to this topic.

1An article is marked at ₹ 3,835. The shopkeeper offers successive discounts of 20% and 50% and earns a profit of ₹ 506. Find the cost price of the article.→ 2A retailer offers a successive discount of 25% and 15% on a TV set marked at Rs. 80,000. What is the final selling price?→ 3A trader sold goods for ₹1250 at a profit of 25% . What was the cost price?→ 4A person earns 25 percent profit on selling price. What will be his profit percentage on the cost price?→ 5On selling an article at (15/17) of the marked price there is a profit of 40 percent. What will be the ratio of marked price of the article to its cost price of the article?→ 6Determine the largest number that divides both 1058 and 1550, leaving remainders of 5 and 11, respectively.→ 784P6 is divisible by 6. Which of the following cannot be the value of P?→ 8The cost price of a whiteboard is ₹2,800. The shopkeeper gave 87% of discount on the cost price. What is the selling price (in ₹)?→ 9Selling price of an article is Rs. 3500. If the value of the loss is Rs. 500, then what is the loss percentage?→ 10A bag is marked at ₹750. If sold at a 10% discount, what is the selling price?→

Simple Interest Doubling and Tripling Quick Quiz

Attempt 5 questions and check your score instantly.

Quick Revision Notes

Simple Interest Doubling and Tripling: Quick Revision

Use these formulas and rules for direct calculations.

  • SI = PRT/100 and A = P + SI.
  • For doubling, SI = P and T = 100/R.
  • For tripling, SI = 2P and T = 200/R.
  • Tripling time is twice the doubling time at the same rate.
  • The principal does not affect doubling or tripling time.
  • For A = kP, T = 100(k - 1)/R.
  • If R is given per month, T = 100/R or 200/R is obtained in months; keep the rate and time units consistent.

Simple Interest Doubling and Tripling FAQs

What is the SI doubling time formula?

The SI doubling time formula is T = 100/R years, where R is the annual rate in percent. It follows because the interest required for doubling is equal to the principal.

What is the SI tripling time formula?

The SI tripling time formula is T = 200/R years, where R is the annual rate in percent. Tripling requires interest equal to twice the principal.

A sum doubles in 15 years under simple interest. What is the rate?

R = 100/T = 100/15 = 20/3%, or approximately 6.67% per annum.

If a sum doubles in 9 years, when will it triple at the same simple interest rate?

Tripling takes twice the doubling time. Therefore, the sum will triple in 18 years.

Does the principal affect the time required for doubling under simple interest?

No. In PRT/100 = P, the principal cancels, giving T = 100/R. Thus, the time depends only on the rate.

How is simple interest doubling different from compound interest doubling?

For simple interest, doubling time is exactly 100/R years. For compound interest, interest is added to the principal periodically, so the doubling time depends on the compounding frequency and is not generally 100/R.

Continue learning Simple Interest Doubling and Tripling on PrepShots

Continue on PrepShots