Simple Interest
MCQs Math

Question:     In how much time a principal of $3100 will amount to $3596 at a simple interest of 4% per annum?

Correct Answer  4

Solution And Explanation

Solution

Given,

Principal (P) = $3100

Rate of Simple Interest (R) = 4% per annum

Amount (A) = $3596

Thus, time (T) = ?

Method (1) Using Formula

Calculation of Simple Interest, when Principal and Amount are given

Formual to Calculate Simple Interest when Principal and Amount are given

We know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $3596 – $3100 = $496

Thus, Simple Interest = $496

Calculation of the Time using forumula when Amount, Simple Interest and Principal are known

Formula to find the Time (T)

Time (T) = ^{100 × Simple Interest}/_{Principal × Rate of Interest}

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 496}/_{3100 × 4}

= ⁴⁹⁶⁰⁰/₁₂₄₀₀

= 4 years (using formula)

Thus, Time (T) = 4 years (from time taken before calculation)Answer

Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known

Here, we have

Principal (P) = $3100

Rate of Simple Interest (R) = 4% per annum

Simple Interest = $496 (As calculated above by subtracting Principal from the Amount given)

We know that, interest is calculated on the basis of the Principal.

This means Simple Interest for 1 year = Rate of simple interest × Principal

Thus, Simple Interest for 1 year = 4% of Principal

= 4% of $3100

= ⁴/₁₀₀ × 3100

= ^{4 × 3100}/₁₀₀

= ¹²⁴⁰⁰/₁₀₀ = 124

Thus, simple Interest for 1 year = $124

Now,

∵ If the simple Interest is $124, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₁₂₄ years

∴ If the simple Interest is $496, then the time = ¹/₁₂₄ × 496 years

= ^{1 × 496}/₁₂₄ years

= ⁴⁹⁶/₁₂₄ = 4 years

Thus, time (T) = 4 years Answer