mcqs Math Simple Interest In how much time a principal of $3150 will amount to $3402 at a simple interest of 4% per annum? 7207

Question: In how much time a principal of $3150 will amount to $3402 at a simple interest of 4% per annum?

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

Correct Answer 2

Solution And Explanation

Solution

Given,

Principal (P) = $3150

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

Amount (A) = $3402

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $3402 – $3150 = $252

Thus, Simple Interest = $252

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 252}/_{3150 × 4}

= ²⁵²⁰⁰/₁₂₆₀₀

= 2 years (using formula)

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

Here, we have

Principal (P) = $3150

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

Simple Interest = $252 (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 $3150

= ⁴/₁₀₀ × 3150

= ^{4 × 3150}/₁₀₀

= ¹²⁶⁰⁰/₁₀₀ = 126

Thus, simple Interest for 1 year = $126

Now,

∵ If the simple Interest is $126, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₁₂₆ years

∴ If the simple Interest is $252, then the time = ¹/₁₂₆ × 252 years

= ^{1 × 252}/₁₂₆ years

= ²⁵²/₁₂₆ = 2 years

Thus, time (T) = 2 years Answer