Examoogle • User • info@examoogle.com • EE-2024-8821

Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked

MathematicsSimple & Compound Interest

A sum of money doubles itself in 8 years at simple interest. In how many years will it become 4 times the original amount at the same rate of interest?

16 years

20 years

24 years

32 years

Correct Answer

📐 MA • Math Direct FormulaMathematicsSimple & Compound Interest

Option C

24 years

Quick Summary:

Use the formula: $\frac{T_1}{T_2} = \frac{n_1 - 1}{n_2 - 1}$ . Here, $\frac{8}{T_2} = \frac{2-1}{4-1}$ , which leads to $T_2 = 8 \times 3 = 24$ years.

📐MAMath SolutionDirect Formula

📋 Given

A sum of money doubles itself (Amount = 2P) in 8 years at simple interest.

🔢 Formula Used

SI=P×R×T100SI = \frac{P \times R \times T}{100}SI=100P×R×T​

⚡ Exam Hall Shortcut / Speed Trick

Use the formula: $\frac{T_1}{T_2} = \frac{n_1 - 1}{n_2 - 1}$ . Here, $\frac{8}{T_2} = \frac{2-1}{4-1}$ , which leads to $T_2 = 8 \times 3 = 24$ years.

⚠️ Common Student Trap / Pitfall

Students often calculate the time to earn 4 times the interest, forgetting that the principal is already part of the total amount (n-1 interest needed).

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Calculate rate of interest

If the sum doubles, the Simple Interest (SI) is equal to the principal (P). Using $SI = P$ and $T = 8$ years:

P=P×R×8100  ⟹  R=1008=12.5%P = \frac{P \times R \times 8}{100} \implies R = \frac{100}{8} = 12.5\%P=100P×R×8​⟹R=8100​=12.5%

Find time for 4 times the amount

To make the amount 4 times the principal, the interest must be 3 times the principal ( $SI = 3P$ ).

3P=P×12.5×T1003P = \frac{P \times 12.5 \times T}{100}3P=100P×12.5×T​

Solve for Time

Solving for T by canceling P from both sides:

T=30012.5=24T = \frac{300}{12.5} = 24T=12.5300​=24

✅

C is correct because the interest required to make the sum 4 times is 3 times the principal, which takes 3 times the duration of doubling.

Core Concepts Used

Click any tag to open in AI Tutor

Simple Interest Principal and Amount relation Linear growth of interest

💡 EXAM TIP

This concept of proportional growth is identical to how you calculate time for maturity in simple annuity problems.

Discussion (0)

Loading discussion...

Prev Next

Correct Answer

Related Questions

Discussion (0)