mcqs Math Simple Interest In how much time a principal of $3100 will amount to $3224 at a simple interest of 2% per annum? 7196

Question: In how much time a principal of $3100 will amount to $3224 at a simple interest of 2% per annum?

(A)  1.5
(B)  2.5
(C)  2
(D)  3

Correct Answer 2

Solution And Explanation

Solution

Given,

Principal (P) = $3100

Rate of Simple Interest (R) = 2% per annum

Amount (A) = $3224

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $3224 – $3100 = $124

Thus, Simple Interest = $124

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 124}/_{3100 × 2}

= ¹²⁴⁰⁰/₆₂₀₀

= 2 years (using formula)

Thus, Time (T) = 2 years (from time taken before calculation)Answer

Here, we have

Principal (P) = $3100

Rate of Simple Interest (R) = 2% per annum

Simple Interest = $124 (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 = 2% of Principal

= 2% of $3100

= ²/₁₀₀ × 3100

= ^{2 × 3100}/₁₀₀

= ⁶²⁰⁰/₁₀₀ = 62

Thus, simple Interest for 1 year = $62

Now,

∵ If the simple Interest is $62, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₂ years

∴ If the simple Interest is $124, then the time = ¹/₆₂ × 124 years

= ^{1 × 124}/₆₂ years

= ¹²⁴/₆₂ = 2 years

Thus, time (T) = 2 years Answer