mcqs Math Simple Interest In how much time a principal of $3050 will amount to $3172 at a simple interest of 2% per annum? 7195

Question: In how much time a principal of $3050 will amount to $3172 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) = $3050

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

Amount (A) = $3172

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $3172 – $3050 = $122

Thus, Simple Interest = $122

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 122}/_{3050 × 2}

= ¹²²⁰⁰/₆₁₀₀

= 2 years (using formula)

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

Here, we have

Principal (P) = $3050

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

Simple Interest = $122 (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 $3050

= ²/₁₀₀ × 3050

= ^{2 × 3050}/₁₀₀

= ⁶¹⁰⁰/₁₀₀ = 61

Thus, simple Interest for 1 year = $61

Now,

∵ If the simple Interest is $61, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₁ years

∴ If the simple Interest is $122, then the time = ¹/₆₁ × 122 years

= ^{1 × 122}/₆₁ years

= ¹²²/₆₁ = 2 years

Thus, time (T) = 2 years Answer